MAYBE 928.45/297.07 MAYBE 928.45/297.07 928.45/297.07 We are left with following problem, upon which TcT provides the 928.45/297.07 certificate MAYBE. 928.45/297.07 928.45/297.07 Strict Trs: 928.45/297.07 { a__a() -> a__c() 928.45/297.07 , a__a() -> a__d() 928.45/297.07 , a__a() -> a() 928.45/297.07 , a__c() -> e() 928.45/297.07 , a__c() -> l() 928.45/297.07 , a__c() -> c() 928.45/297.07 , a__b() -> a__c() 928.45/297.07 , a__b() -> a__d() 928.45/297.07 , a__b() -> b() 928.45/297.07 , a__k() -> l() 928.45/297.07 , a__k() -> m() 928.45/297.07 , a__k() -> k() 928.45/297.07 , a__d() -> m() 928.45/297.07 , a__d() -> d() 928.45/297.07 , a__A() -> a__h(a__f(a__a()), a__f(a__b())) 928.45/297.07 , a__A() -> A() 928.45/297.07 , a__h(X, X) -> a__g(mark(X), mark(X), a__f(a__k())) 928.45/297.07 , a__h(X1, X2) -> h(X1, X2) 928.45/297.07 , a__f(X) -> a__z(mark(X), X) 928.45/297.07 , a__f(X) -> f(X) 928.45/297.07 , a__g(X1, X2, X3) -> g(X1, X2, X3) 928.45/297.07 , a__g(d(), X, X) -> a__A() 928.45/297.07 , mark(e()) -> e() 928.45/297.07 , mark(l()) -> l() 928.45/297.07 , mark(m()) -> m() 928.45/297.07 , mark(d()) -> a__d() 928.45/297.07 , mark(A()) -> a__A() 928.45/297.07 , mark(a()) -> a__a() 928.45/297.07 , mark(b()) -> a__b() 928.45/297.07 , mark(c()) -> a__c() 928.45/297.07 , mark(k()) -> a__k() 928.45/297.07 , mark(z(X1, X2)) -> a__z(mark(X1), X2) 928.45/297.07 , mark(f(X)) -> a__f(mark(X)) 928.45/297.07 , mark(h(X1, X2)) -> a__h(mark(X1), mark(X2)) 928.45/297.07 , mark(g(X1, X2, X3)) -> a__g(mark(X1), mark(X2), mark(X3)) 928.45/297.07 , a__z(X1, X2) -> z(X1, X2) 928.45/297.07 , a__z(e(), X) -> mark(X) } 928.45/297.07 Obligation: 928.45/297.07 innermost runtime complexity 928.45/297.07 Answer: 928.45/297.07 MAYBE 928.45/297.07 928.45/297.07 None of the processors succeeded. 928.45/297.07 928.45/297.07 Details of failed attempt(s): 928.45/297.07 ----------------------------- 928.45/297.07 1) 'empty' failed due to the following reason: 928.45/297.07 928.45/297.07 Empty strict component of the problem is NOT empty. 928.45/297.07 928.45/297.07 2) 'Best' failed due to the following reason: 928.45/297.07 928.45/297.07 None of the processors succeeded. 928.45/297.07 928.45/297.07 Details of failed attempt(s): 928.45/297.07 ----------------------------- 928.45/297.07 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 928.45/297.07 following reason: 928.45/297.07 928.45/297.07 Computation stopped due to timeout after 297.0 seconds. 928.45/297.07 928.45/297.07 2) 'Best' failed due to the following reason: 928.45/297.07 928.45/297.07 None of the processors succeeded. 928.45/297.07 928.45/297.07 Details of failed attempt(s): 928.45/297.07 ----------------------------- 928.45/297.07 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 928.45/297.07 seconds)' failed due to the following reason: 928.45/297.07 928.45/297.07 The weightgap principle applies (using the following nonconstant 928.45/297.07 growth matrix-interpretation) 928.45/297.07 928.45/297.07 The following argument positions are usable: 928.45/297.07 Uargs(a__h) = {1, 2}, Uargs(a__f) = {1}, Uargs(a__g) = {1, 2, 3}, 928.45/297.07 Uargs(a__z) = {1} 928.45/297.07 928.45/297.07 TcT has computed the following matrix interpretation satisfying 928.45/297.07 not(EDA) and not(IDA(1)). 928.45/297.07 928.45/297.07 [a__a] = [6] 928.45/297.07 928.45/297.07 [a__c] = [7] 928.45/297.07 928.45/297.07 [a__b] = [3] 928.45/297.07 928.45/297.07 [e] = [7] 928.45/297.07 928.45/297.07 [a__k] = [4] 928.45/297.07 928.45/297.07 [l] = [2] 928.45/297.07 928.45/297.07 [a__d] = [7] 928.45/297.07 928.45/297.07 [m] = [2] 928.45/297.07 928.45/297.07 [a__A] = [7] 928.45/297.07 928.45/297.07 [a__h](x1, x2) = [1] x1 + [1] x2 + [0] 928.45/297.07 928.45/297.07 [a__f](x1) = [1] x1 + [3] 928.45/297.07 928.45/297.07 [a__g](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [1] 928.45/297.07 928.45/297.07 [mark](x1) = [3] 928.45/297.07 928.45/297.07 [d] = [3] 928.45/297.07 928.45/297.07 [a__z](x1, x2) = [1] x1 + [7] 928.45/297.07 928.45/297.07 [A] = [6] 928.45/297.07 928.45/297.07 [a] = [5] 928.45/297.07 928.45/297.07 [b] = [2] 928.45/297.07 928.45/297.07 [c] = [6] 928.45/297.07 928.45/297.07 [k] = [3] 928.45/297.07 928.45/297.07 [z](x1, x2) = [1] x1 + [6] 928.45/297.07 928.45/297.07 [f](x1) = [1] x1 + [2] 928.45/297.07 928.45/297.07 [h](x1, x2) = [1] x1 + [1] x2 + [7] 928.45/297.07 928.45/297.07 [g](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 928.45/297.07 928.45/297.07 The order satisfies the following ordering constraints: 928.45/297.07 928.45/297.07 [a__a()] = [6] 928.45/297.07 ? [7] 928.45/297.07 = [a__c()] 928.45/297.07 928.45/297.07 [a__a()] = [6] 928.45/297.07 ? [7] 928.45/297.07 = [a__d()] 928.45/297.07 928.45/297.07 [a__a()] = [6] 928.45/297.07 > [5] 928.45/297.07 = [a()] 928.45/297.07 928.45/297.07 [a__c()] = [7] 928.45/297.07 >= [7] 928.45/297.07 = [e()] 928.45/297.07 928.45/297.07 [a__c()] = [7] 928.45/297.07 > [2] 928.45/297.07 = [l()] 928.45/297.07 928.45/297.07 [a__c()] = [7] 928.45/297.07 > [6] 928.45/297.07 = [c()] 928.45/297.07 928.45/297.07 [a__b()] = [3] 928.45/297.07 ? [7] 928.45/297.07 = [a__c()] 928.45/297.07 928.45/297.07 [a__b()] = [3] 928.45/297.07 ? [7] 928.45/297.07 = [a__d()] 928.45/297.07 928.45/297.07 [a__b()] = [3] 928.45/297.07 > [2] 928.45/297.07 = [b()] 928.45/297.07 928.45/297.07 [a__k()] = [4] 928.45/297.07 > [2] 928.45/297.07 = [l()] 928.45/297.07 928.45/297.07 [a__k()] = [4] 928.45/297.07 > [2] 928.45/297.07 = [m()] 928.45/297.07 928.45/297.07 [a__k()] = [4] 928.45/297.07 > [3] 928.45/297.07 = [k()] 928.45/297.07 928.45/297.07 [a__d()] = [7] 928.45/297.07 > [2] 928.45/297.07 = [m()] 928.45/297.07 928.45/297.07 [a__d()] = [7] 928.45/297.07 > [3] 928.45/297.07 = [d()] 928.45/297.07 928.45/297.07 [a__A()] = [7] 928.45/297.07 ? [15] 928.45/297.07 = [a__h(a__f(a__a()), a__f(a__b()))] 928.45/297.07 928.45/297.07 [a__A()] = [7] 928.45/297.07 > [6] 928.45/297.07 = [A()] 928.45/297.07 928.45/297.07 [a__h(X, X)] = [2] X + [0] 928.45/297.07 ? [14] 928.45/297.07 = [a__g(mark(X), mark(X), a__f(a__k()))] 928.45/297.07 928.45/297.07 [a__h(X1, X2)] = [1] X1 + [1] X2 + [0] 928.45/297.07 ? [1] X1 + [1] X2 + [7] 928.45/297.07 = [h(X1, X2)] 928.45/297.07 928.45/297.07 [a__f(X)] = [1] X + [3] 928.45/297.07 ? [10] 928.45/297.07 = [a__z(mark(X), X)] 928.45/297.07 928.45/297.07 [a__f(X)] = [1] X + [3] 928.45/297.07 > [1] X + [2] 928.45/297.07 = [f(X)] 928.45/297.07 928.45/297.07 [a__g(X1, X2, X3)] = [1] X1 + [1] X2 + [1] X3 + [1] 928.45/297.07 > [1] X1 + [1] X2 + [1] X3 + [0] 928.45/297.07 = [g(X1, X2, X3)] 928.45/297.07 928.45/297.07 [a__g(d(), X, X)] = [2] X + [4] 928.45/297.07 ? [7] 928.45/297.07 = [a__A()] 928.45/297.07 928.45/297.07 [mark(e())] = [3] 928.45/297.07 ? [7] 928.45/297.07 = [e()] 928.45/297.07 928.45/297.07 [mark(l())] = [3] 928.45/297.07 > [2] 928.45/297.07 = [l()] 928.45/297.07 928.45/297.07 [mark(m())] = [3] 928.45/297.07 > [2] 928.45/297.07 = [m()] 928.45/297.07 928.45/297.07 [mark(d())] = [3] 928.45/297.07 ? [7] 928.45/297.07 = [a__d()] 928.45/297.07 928.45/297.07 [mark(A())] = [3] 928.45/297.07 ? [7] 928.45/297.07 = [a__A()] 928.45/297.07 928.45/297.07 [mark(a())] = [3] 928.45/297.07 ? [6] 928.45/297.07 = [a__a()] 928.45/297.07 928.45/297.07 [mark(b())] = [3] 928.45/297.07 >= [3] 928.45/297.07 = [a__b()] 928.45/297.07 928.45/297.07 [mark(c())] = [3] 928.45/297.07 ? [7] 928.45/297.07 = [a__c()] 928.45/297.07 928.45/297.07 [mark(k())] = [3] 928.45/297.07 ? [4] 928.45/297.07 = [a__k()] 928.45/297.07 928.45/297.07 [mark(z(X1, X2))] = [3] 928.45/297.07 ? [10] 928.45/297.07 = [a__z(mark(X1), X2)] 928.45/297.07 928.45/297.07 [mark(f(X))] = [3] 928.45/297.07 ? [6] 928.45/297.07 = [a__f(mark(X))] 928.45/297.07 928.45/297.07 [mark(h(X1, X2))] = [3] 928.45/297.07 ? [6] 928.45/297.07 = [a__h(mark(X1), mark(X2))] 928.45/297.07 928.45/297.07 [mark(g(X1, X2, X3))] = [3] 928.45/297.07 ? [10] 928.45/297.07 = [a__g(mark(X1), mark(X2), mark(X3))] 928.45/297.07 928.45/297.07 [a__z(X1, X2)] = [1] X1 + [7] 928.45/297.07 > [1] X1 + [6] 928.45/297.07 = [z(X1, X2)] 928.45/297.07 928.45/297.08 [a__z(e(), X)] = [14] 928.45/297.08 > [3] 928.45/297.08 = [mark(X)] 928.45/297.08 928.45/297.08 928.45/297.08 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 928.45/297.08 928.45/297.08 We are left with following problem, upon which TcT provides the 928.45/297.08 certificate MAYBE. 928.45/297.08 928.45/297.08 Strict Trs: 928.45/297.08 { a__a() -> a__c() 928.45/297.08 , a__a() -> a__d() 928.45/297.08 , a__c() -> e() 928.45/297.08 , a__b() -> a__c() 928.45/297.08 , a__b() -> a__d() 928.45/297.08 , a__A() -> a__h(a__f(a__a()), a__f(a__b())) 928.45/297.08 , a__h(X, X) -> a__g(mark(X), mark(X), a__f(a__k())) 928.45/297.08 , a__h(X1, X2) -> h(X1, X2) 928.45/297.08 , a__f(X) -> a__z(mark(X), X) 928.45/297.08 , a__g(d(), X, X) -> a__A() 928.45/297.08 , mark(e()) -> e() 928.45/297.08 , mark(d()) -> a__d() 928.45/297.08 , mark(A()) -> a__A() 928.45/297.08 , mark(a()) -> a__a() 928.45/297.08 , mark(b()) -> a__b() 928.45/297.08 , mark(c()) -> a__c() 928.45/297.08 , mark(k()) -> a__k() 928.45/297.08 , mark(z(X1, X2)) -> a__z(mark(X1), X2) 928.45/297.08 , mark(f(X)) -> a__f(mark(X)) 928.45/297.08 , mark(h(X1, X2)) -> a__h(mark(X1), mark(X2)) 928.45/297.08 , mark(g(X1, X2, X3)) -> a__g(mark(X1), mark(X2), mark(X3)) } 928.45/297.08 Weak Trs: 928.45/297.08 { a__a() -> a() 928.45/297.08 , a__c() -> l() 928.45/297.08 , a__c() -> c() 928.45/297.08 , a__b() -> b() 928.45/297.08 , a__k() -> l() 928.45/297.08 , a__k() -> m() 928.45/297.08 , a__k() -> k() 928.45/297.08 , a__d() -> m() 928.45/297.08 , a__d() -> d() 928.45/297.08 , a__A() -> A() 928.45/297.08 , a__f(X) -> f(X) 928.45/297.08 , a__g(X1, X2, X3) -> g(X1, X2, X3) 928.45/297.08 , mark(l()) -> l() 928.45/297.08 , mark(m()) -> m() 928.45/297.08 , a__z(X1, X2) -> z(X1, X2) 928.45/297.08 , a__z(e(), X) -> mark(X) } 928.45/297.08 Obligation: 928.45/297.08 innermost runtime complexity 928.45/297.08 Answer: 928.45/297.08 MAYBE 928.45/297.08 928.45/297.08 The weightgap principle applies (using the following nonconstant 928.45/297.08 growth matrix-interpretation) 928.45/297.08 928.45/297.08 The following argument positions are usable: 928.45/297.08 Uargs(a__h) = {1, 2}, Uargs(a__f) = {1}, Uargs(a__g) = {1, 2, 3}, 928.45/297.08 Uargs(a__z) = {1} 928.45/297.08 928.45/297.08 TcT has computed the following matrix interpretation satisfying 928.45/297.08 not(EDA) and not(IDA(1)). 928.45/297.08 928.45/297.08 [a__a] = [4] 928.45/297.08 928.45/297.08 [a__c] = [1] 928.45/297.08 928.45/297.08 [a__b] = [0] 928.45/297.08 928.45/297.08 [e] = [4] 928.45/297.08 928.45/297.08 [a__k] = [0] 928.45/297.08 928.45/297.08 [l] = [0] 928.45/297.08 928.45/297.08 [a__d] = [4] 928.45/297.08 928.45/297.08 [m] = [0] 928.45/297.08 928.45/297.08 [a__A] = [0] 928.45/297.08 928.45/297.08 [a__h](x1, x2) = [1] x1 + [1] x2 + [0] 928.45/297.08 928.45/297.08 [a__f](x1) = [1] x1 + [0] 928.45/297.08 928.45/297.08 [a__g](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 928.45/297.08 928.45/297.08 [mark](x1) = [0] 928.45/297.08 928.45/297.08 [d] = [1] 928.45/297.08 928.45/297.08 [a__z](x1, x2) = [1] x1 + [0] 928.45/297.08 928.45/297.08 [A] = [0] 928.45/297.08 928.45/297.08 [a] = [4] 928.45/297.08 928.45/297.08 [b] = [0] 928.45/297.08 928.45/297.08 [c] = [1] 928.45/297.08 928.45/297.08 [k] = [0] 928.45/297.08 928.45/297.08 [z](x1, x2) = [1] x1 + [0] 928.45/297.08 928.45/297.08 [f](x1) = [1] x1 + [0] 928.45/297.08 928.45/297.08 [h](x1, x2) = [1] x1 + [1] x2 + [7] 928.45/297.08 928.45/297.08 [g](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 928.45/297.08 928.45/297.08 The order satisfies the following ordering constraints: 928.45/297.08 928.45/297.08 [a__a()] = [4] 928.45/297.08 > [1] 928.45/297.08 = [a__c()] 928.45/297.08 928.45/297.08 [a__a()] = [4] 928.45/297.08 >= [4] 928.45/297.08 = [a__d()] 928.45/297.08 928.45/297.08 [a__a()] = [4] 928.45/297.08 >= [4] 928.45/297.08 = [a()] 928.45/297.08 928.45/297.08 [a__c()] = [1] 928.45/297.08 ? [4] 928.45/297.08 = [e()] 928.45/297.08 928.45/297.08 [a__c()] = [1] 928.45/297.08 > [0] 928.45/297.08 = [l()] 928.45/297.08 928.45/297.08 [a__c()] = [1] 928.45/297.08 >= [1] 928.45/297.08 = [c()] 928.45/297.08 928.45/297.08 [a__b()] = [0] 928.45/297.08 ? [1] 928.45/297.08 = [a__c()] 928.45/297.08 928.45/297.08 [a__b()] = [0] 928.45/297.08 ? [4] 928.45/297.08 = [a__d()] 928.45/297.08 928.45/297.08 [a__b()] = [0] 928.45/297.08 >= [0] 928.45/297.08 = [b()] 928.45/297.08 928.45/297.08 [a__k()] = [0] 928.45/297.08 >= [0] 928.45/297.08 = [l()] 928.45/297.08 928.45/297.08 [a__k()] = [0] 928.45/297.08 >= [0] 928.45/297.08 = [m()] 928.45/297.08 928.45/297.08 [a__k()] = [0] 928.45/297.08 >= [0] 928.45/297.08 = [k()] 928.45/297.08 928.45/297.08 [a__d()] = [4] 928.45/297.08 > [0] 928.45/297.08 = [m()] 928.45/297.08 928.45/297.08 [a__d()] = [4] 928.45/297.08 > [1] 928.45/297.08 = [d()] 928.45/297.08 928.45/297.08 [a__A()] = [0] 928.45/297.08 ? [4] 928.45/297.08 = [a__h(a__f(a__a()), a__f(a__b()))] 928.45/297.08 928.45/297.08 [a__A()] = [0] 928.45/297.08 >= [0] 928.45/297.08 = [A()] 928.45/297.08 928.45/297.08 [a__h(X, X)] = [2] X + [0] 928.45/297.08 >= [0] 928.45/297.08 = [a__g(mark(X), mark(X), a__f(a__k()))] 928.45/297.08 928.45/297.08 [a__h(X1, X2)] = [1] X1 + [1] X2 + [0] 928.45/297.08 ? [1] X1 + [1] X2 + [7] 928.45/297.08 = [h(X1, X2)] 928.45/297.08 928.45/297.08 [a__f(X)] = [1] X + [0] 928.45/297.08 >= [0] 928.45/297.08 = [a__z(mark(X), X)] 928.45/297.08 928.45/297.08 [a__f(X)] = [1] X + [0] 928.45/297.08 >= [1] X + [0] 928.45/297.08 = [f(X)] 928.45/297.08 928.45/297.08 [a__g(X1, X2, X3)] = [1] X1 + [1] X2 + [1] X3 + [0] 928.45/297.08 >= [1] X1 + [1] X2 + [1] X3 + [0] 928.45/297.08 = [g(X1, X2, X3)] 928.45/297.08 928.45/297.08 [a__g(d(), X, X)] = [2] X + [1] 928.45/297.08 > [0] 928.45/297.08 = [a__A()] 928.45/297.08 928.45/297.08 [mark(e())] = [0] 928.45/297.08 ? [4] 928.45/297.08 = [e()] 928.45/297.08 928.45/297.08 [mark(l())] = [0] 928.45/297.08 >= [0] 928.45/297.08 = [l()] 928.45/297.08 928.45/297.08 [mark(m())] = [0] 928.45/297.08 >= [0] 928.45/297.08 = [m()] 928.45/297.08 928.45/297.08 [mark(d())] = [0] 928.45/297.08 ? [4] 928.45/297.08 = [a__d()] 928.45/297.08 928.45/297.08 [mark(A())] = [0] 928.45/297.08 >= [0] 928.45/297.08 = [a__A()] 928.45/297.08 928.45/297.08 [mark(a())] = [0] 928.45/297.08 ? [4] 928.45/297.08 = [a__a()] 928.45/297.08 928.45/297.08 [mark(b())] = [0] 928.45/297.08 >= [0] 928.45/297.08 = [a__b()] 928.45/297.08 928.45/297.08 [mark(c())] = [0] 928.45/297.08 ? [1] 928.45/297.08 = [a__c()] 928.45/297.08 928.45/297.08 [mark(k())] = [0] 928.45/297.08 >= [0] 928.45/297.08 = [a__k()] 928.45/297.08 928.45/297.08 [mark(z(X1, X2))] = [0] 928.45/297.08 >= [0] 928.45/297.08 = [a__z(mark(X1), X2)] 928.45/297.08 928.45/297.08 [mark(f(X))] = [0] 928.45/297.08 >= [0] 928.45/297.08 = [a__f(mark(X))] 928.45/297.08 928.45/297.08 [mark(h(X1, X2))] = [0] 928.45/297.08 >= [0] 928.45/297.08 = [a__h(mark(X1), mark(X2))] 928.45/297.08 928.45/297.08 [mark(g(X1, X2, X3))] = [0] 928.45/297.08 >= [0] 928.45/297.08 = [a__g(mark(X1), mark(X2), mark(X3))] 928.45/297.08 928.45/297.08 [a__z(X1, X2)] = [1] X1 + [0] 928.45/297.08 >= [1] X1 + [0] 928.45/297.08 = [z(X1, X2)] 928.45/297.08 928.45/297.08 [a__z(e(), X)] = [4] 928.45/297.08 > [0] 928.45/297.08 = [mark(X)] 928.45/297.08 928.45/297.08 928.45/297.08 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 928.45/297.08 928.45/297.08 We are left with following problem, upon which TcT provides the 928.45/297.08 certificate MAYBE. 928.45/297.08 928.45/297.08 Strict Trs: 928.45/297.08 { a__a() -> a__d() 928.45/297.08 , a__c() -> e() 928.45/297.08 , a__b() -> a__c() 928.45/297.08 , a__b() -> a__d() 928.45/297.08 , a__A() -> a__h(a__f(a__a()), a__f(a__b())) 928.45/297.08 , a__h(X, X) -> a__g(mark(X), mark(X), a__f(a__k())) 928.45/297.08 , a__h(X1, X2) -> h(X1, X2) 928.45/297.08 , a__f(X) -> a__z(mark(X), X) 928.45/297.08 , mark(e()) -> e() 928.45/297.08 , mark(d()) -> a__d() 928.45/297.08 , mark(A()) -> a__A() 928.45/297.08 , mark(a()) -> a__a() 928.45/297.08 , mark(b()) -> a__b() 928.45/297.08 , mark(c()) -> a__c() 928.45/297.08 , mark(k()) -> a__k() 928.45/297.08 , mark(z(X1, X2)) -> a__z(mark(X1), X2) 928.45/297.08 , mark(f(X)) -> a__f(mark(X)) 928.45/297.08 , mark(h(X1, X2)) -> a__h(mark(X1), mark(X2)) 928.45/297.08 , mark(g(X1, X2, X3)) -> a__g(mark(X1), mark(X2), mark(X3)) } 928.45/297.08 Weak Trs: 928.45/297.08 { a__a() -> a__c() 928.45/297.08 , a__a() -> a() 928.45/297.08 , a__c() -> l() 928.45/297.08 , a__c() -> c() 928.45/297.08 , a__b() -> b() 928.45/297.08 , a__k() -> l() 928.45/297.08 , a__k() -> m() 928.45/297.08 , a__k() -> k() 928.45/297.08 , a__d() -> m() 928.45/297.08 , a__d() -> d() 928.45/297.08 , a__A() -> A() 928.45/297.08 , a__f(X) -> f(X) 928.45/297.08 , a__g(X1, X2, X3) -> g(X1, X2, X3) 928.45/297.08 , a__g(d(), X, X) -> a__A() 928.45/297.08 , mark(l()) -> l() 928.45/297.08 , mark(m()) -> m() 928.45/297.08 , a__z(X1, X2) -> z(X1, X2) 928.45/297.08 , a__z(e(), X) -> mark(X) } 928.45/297.08 Obligation: 928.45/297.08 innermost runtime complexity 928.45/297.08 Answer: 928.45/297.08 MAYBE 928.45/297.08 928.45/297.08 The weightgap principle applies (using the following nonconstant 928.45/297.08 growth matrix-interpretation) 928.45/297.08 928.45/297.08 The following argument positions are usable: 928.45/297.08 Uargs(a__h) = {1, 2}, Uargs(a__f) = {1}, Uargs(a__g) = {1, 2, 3}, 928.45/297.08 Uargs(a__z) = {1} 928.45/297.08 928.45/297.08 TcT has computed the following matrix interpretation satisfying 928.45/297.08 not(EDA) and not(IDA(1)). 928.45/297.08 928.45/297.08 [a__a] = [6] 928.45/297.08 928.45/297.08 [a__c] = [1] 928.45/297.08 928.45/297.08 [a__b] = [0] 928.45/297.08 928.45/297.08 [e] = [4] 928.45/297.08 928.45/297.08 [a__k] = [0] 928.45/297.08 928.45/297.08 [l] = [0] 928.45/297.08 928.45/297.08 [a__d] = [4] 928.45/297.08 928.45/297.08 [m] = [0] 928.45/297.08 928.45/297.08 [a__A] = [1] 928.45/297.08 928.45/297.08 [a__h](x1, x2) = [1] x1 + [1] x2 + [0] 928.45/297.08 928.45/297.08 [a__f](x1) = [1] x1 + [0] 928.45/297.08 928.45/297.08 [a__g](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 928.45/297.08 928.45/297.08 [mark](x1) = [0] 928.45/297.08 928.45/297.08 [d] = [4] 928.45/297.08 928.45/297.08 [a__z](x1, x2) = [1] x1 + [0] 928.45/297.08 928.45/297.08 [A] = [1] 928.45/297.08 928.45/297.08 [a] = [5] 928.45/297.08 928.45/297.08 [b] = [0] 928.45/297.08 928.45/297.08 [c] = [1] 928.45/297.08 928.45/297.08 [k] = [0] 928.45/297.08 928.45/297.08 [z](x1, x2) = [1] x1 + [0] 928.45/297.08 928.45/297.08 [f](x1) = [1] x1 + [0] 928.45/297.08 928.45/297.08 [h](x1, x2) = [1] x1 + [1] x2 + [7] 928.45/297.08 928.45/297.08 [g](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 928.45/297.08 928.45/297.08 The order satisfies the following ordering constraints: 928.45/297.08 928.45/297.08 [a__a()] = [6] 928.45/297.08 > [1] 928.45/297.08 = [a__c()] 928.45/297.08 928.45/297.08 [a__a()] = [6] 928.45/297.08 > [4] 928.45/297.08 = [a__d()] 928.45/297.08 928.45/297.08 [a__a()] = [6] 928.45/297.08 > [5] 928.45/297.08 = [a()] 928.45/297.08 928.45/297.08 [a__c()] = [1] 928.45/297.08 ? [4] 928.45/297.08 = [e()] 928.45/297.08 928.45/297.08 [a__c()] = [1] 928.45/297.08 > [0] 928.45/297.08 = [l()] 928.45/297.08 928.45/297.08 [a__c()] = [1] 928.45/297.08 >= [1] 928.45/297.08 = [c()] 928.45/297.08 928.45/297.08 [a__b()] = [0] 928.45/297.08 ? [1] 928.45/297.08 = [a__c()] 928.45/297.08 928.45/297.08 [a__b()] = [0] 928.45/297.08 ? [4] 928.45/297.08 = [a__d()] 928.45/297.08 928.45/297.08 [a__b()] = [0] 928.45/297.08 >= [0] 928.45/297.09 = [b()] 928.45/297.09 928.45/297.09 [a__k()] = [0] 928.45/297.09 >= [0] 928.45/297.09 = [l()] 928.45/297.09 928.45/297.09 [a__k()] = [0] 928.45/297.09 >= [0] 928.45/297.09 = [m()] 928.45/297.09 928.45/297.09 [a__k()] = [0] 928.45/297.09 >= [0] 928.45/297.09 = [k()] 928.45/297.09 928.45/297.09 [a__d()] = [4] 928.45/297.09 > [0] 928.45/297.09 = [m()] 928.45/297.09 928.45/297.09 [a__d()] = [4] 928.45/297.09 >= [4] 928.45/297.09 = [d()] 928.45/297.09 928.45/297.09 [a__A()] = [1] 928.45/297.09 ? [6] 928.45/297.09 = [a__h(a__f(a__a()), a__f(a__b()))] 928.45/297.09 928.45/297.09 [a__A()] = [1] 928.45/297.09 >= [1] 928.45/297.09 = [A()] 928.45/297.09 928.45/297.09 [a__h(X, X)] = [2] X + [0] 928.45/297.09 >= [0] 928.45/297.09 = [a__g(mark(X), mark(X), a__f(a__k()))] 928.45/297.09 928.45/297.09 [a__h(X1, X2)] = [1] X1 + [1] X2 + [0] 928.45/297.09 ? [1] X1 + [1] X2 + [7] 928.45/297.09 = [h(X1, X2)] 928.45/297.09 928.45/297.09 [a__f(X)] = [1] X + [0] 928.45/297.09 >= [0] 928.45/297.09 = [a__z(mark(X), X)] 928.45/297.09 928.45/297.09 [a__f(X)] = [1] X + [0] 928.45/297.09 >= [1] X + [0] 928.45/297.09 = [f(X)] 928.45/297.09 928.45/297.09 [a__g(X1, X2, X3)] = [1] X1 + [1] X2 + [1] X3 + [0] 928.45/297.09 >= [1] X1 + [1] X2 + [1] X3 + [0] 928.45/297.09 = [g(X1, X2, X3)] 928.45/297.09 928.45/297.09 [a__g(d(), X, X)] = [2] X + [4] 928.45/297.09 > [1] 928.45/297.09 = [a__A()] 928.45/297.09 928.45/297.09 [mark(e())] = [0] 928.45/297.09 ? [4] 928.45/297.09 = [e()] 928.45/297.09 928.45/297.09 [mark(l())] = [0] 928.45/297.09 >= [0] 928.45/297.09 = [l()] 928.45/297.09 928.45/297.09 [mark(m())] = [0] 928.45/297.09 >= [0] 928.45/297.09 = [m()] 928.45/297.09 928.45/297.09 [mark(d())] = [0] 928.45/297.09 ? [4] 928.45/297.09 = [a__d()] 928.45/297.09 928.45/297.09 [mark(A())] = [0] 928.45/297.09 ? [1] 928.45/297.09 = [a__A()] 928.45/297.09 928.45/297.09 [mark(a())] = [0] 928.45/297.09 ? [6] 928.45/297.09 = [a__a()] 928.45/297.09 928.45/297.09 [mark(b())] = [0] 928.45/297.09 >= [0] 928.45/297.09 = [a__b()] 928.45/297.09 928.45/297.09 [mark(c())] = [0] 928.45/297.09 ? [1] 928.45/297.09 = [a__c()] 928.45/297.09 928.45/297.09 [mark(k())] = [0] 928.45/297.09 >= [0] 928.45/297.09 = [a__k()] 928.45/297.09 928.45/297.09 [mark(z(X1, X2))] = [0] 928.45/297.09 >= [0] 928.45/297.09 = [a__z(mark(X1), X2)] 928.45/297.09 928.45/297.09 [mark(f(X))] = [0] 928.45/297.09 >= [0] 928.45/297.09 = [a__f(mark(X))] 928.45/297.09 928.45/297.09 [mark(h(X1, X2))] = [0] 928.45/297.09 >= [0] 928.45/297.09 = [a__h(mark(X1), mark(X2))] 928.45/297.09 928.45/297.09 [mark(g(X1, X2, X3))] = [0] 928.45/297.09 >= [0] 928.45/297.09 = [a__g(mark(X1), mark(X2), mark(X3))] 928.45/297.09 928.45/297.09 [a__z(X1, X2)] = [1] X1 + [0] 928.45/297.09 >= [1] X1 + [0] 928.45/297.09 = [z(X1, X2)] 928.45/297.09 928.45/297.09 [a__z(e(), X)] = [4] 928.45/297.09 > [0] 928.45/297.09 = [mark(X)] 928.45/297.09 928.45/297.09 928.45/297.09 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 928.45/297.09 928.45/297.09 We are left with following problem, upon which TcT provides the 928.45/297.09 certificate MAYBE. 928.45/297.09 928.45/297.09 Strict Trs: 928.45/297.09 { a__c() -> e() 928.45/297.09 , a__b() -> a__c() 928.45/297.09 , a__b() -> a__d() 928.45/297.09 , a__A() -> a__h(a__f(a__a()), a__f(a__b())) 928.45/297.09 , a__h(X, X) -> a__g(mark(X), mark(X), a__f(a__k())) 928.45/297.09 , a__h(X1, X2) -> h(X1, X2) 928.45/297.09 , a__f(X) -> a__z(mark(X), X) 928.45/297.09 , mark(e()) -> e() 928.45/297.09 , mark(d()) -> a__d() 928.45/297.09 , mark(A()) -> a__A() 928.45/297.09 , mark(a()) -> a__a() 928.45/297.09 , mark(b()) -> a__b() 928.45/297.09 , mark(c()) -> a__c() 928.45/297.09 , mark(k()) -> a__k() 928.45/297.09 , mark(z(X1, X2)) -> a__z(mark(X1), X2) 928.45/297.09 , mark(f(X)) -> a__f(mark(X)) 928.45/297.09 , mark(h(X1, X2)) -> a__h(mark(X1), mark(X2)) 928.45/297.09 , mark(g(X1, X2, X3)) -> a__g(mark(X1), mark(X2), mark(X3)) } 928.45/297.09 Weak Trs: 928.45/297.09 { a__a() -> a__c() 928.45/297.09 , a__a() -> a__d() 928.45/297.09 , a__a() -> a() 928.45/297.09 , a__c() -> l() 928.45/297.09 , a__c() -> c() 928.45/297.09 , a__b() -> b() 928.45/297.09 , a__k() -> l() 928.45/297.09 , a__k() -> m() 928.45/297.09 , a__k() -> k() 928.45/297.09 , a__d() -> m() 928.45/297.09 , a__d() -> d() 928.45/297.09 , a__A() -> A() 928.45/297.09 , a__f(X) -> f(X) 928.45/297.09 , a__g(X1, X2, X3) -> g(X1, X2, X3) 928.45/297.09 , a__g(d(), X, X) -> a__A() 928.45/297.09 , mark(l()) -> l() 928.45/297.09 , mark(m()) -> m() 928.45/297.09 , a__z(X1, X2) -> z(X1, X2) 928.45/297.09 , a__z(e(), X) -> mark(X) } 928.45/297.09 Obligation: 928.45/297.09 innermost runtime complexity 928.45/297.09 Answer: 928.45/297.09 MAYBE 928.45/297.09 928.45/297.09 The weightgap principle applies (using the following nonconstant 928.45/297.09 growth matrix-interpretation) 928.45/297.09 928.45/297.09 The following argument positions are usable: 928.45/297.09 Uargs(a__h) = {1, 2}, Uargs(a__f) = {1}, Uargs(a__g) = {1, 2, 3}, 928.45/297.09 Uargs(a__z) = {1} 928.45/297.09 928.45/297.09 TcT has computed the following matrix interpretation satisfying 928.45/297.09 not(EDA) and not(IDA(1)). 928.45/297.09 928.45/297.09 [a__a] = [4] 928.45/297.09 928.45/297.09 [a__c] = [0] 928.45/297.09 928.45/297.09 [a__b] = [4] 928.45/297.09 928.45/297.09 [e] = [4] 928.45/297.09 928.45/297.09 [a__k] = [0] 928.45/297.09 928.45/297.09 [l] = [0] 928.45/297.09 928.45/297.09 [a__d] = [4] 928.45/297.09 928.45/297.09 [m] = [0] 928.45/297.09 928.45/297.09 [a__A] = [1] 928.45/297.09 928.45/297.09 [a__h](x1, x2) = [1] x1 + [1] x2 + [0] 928.45/297.09 928.45/297.09 [a__f](x1) = [1] x1 + [0] 928.45/297.09 928.45/297.09 [a__g](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 928.45/297.09 928.45/297.09 [mark](x1) = [0] 928.45/297.09 928.45/297.09 [d] = [4] 928.45/297.09 928.45/297.09 [a__z](x1, x2) = [1] x1 + [0] 928.45/297.09 928.45/297.09 [A] = [1] 928.45/297.09 928.45/297.09 [a] = [4] 928.45/297.09 928.45/297.09 [b] = [4] 928.45/297.09 928.45/297.09 [c] = [0] 928.45/297.09 928.45/297.09 [k] = [0] 928.45/297.09 928.45/297.09 [z](x1, x2) = [1] x1 + [0] 928.45/297.09 928.45/297.09 [f](x1) = [1] x1 + [0] 928.45/297.09 928.45/297.09 [h](x1, x2) = [1] x1 + [1] x2 + [7] 928.45/297.09 928.45/297.09 [g](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 928.45/297.09 928.45/297.09 The order satisfies the following ordering constraints: 928.45/297.09 928.45/297.09 [a__a()] = [4] 928.45/297.09 > [0] 928.45/297.09 = [a__c()] 928.45/297.09 928.45/297.09 [a__a()] = [4] 928.45/297.09 >= [4] 928.45/297.09 = [a__d()] 928.45/297.09 928.45/297.09 [a__a()] = [4] 928.45/297.09 >= [4] 928.45/297.09 = [a()] 928.45/297.09 928.45/297.09 [a__c()] = [0] 928.45/297.09 ? [4] 928.45/297.09 = [e()] 928.45/297.09 928.45/297.09 [a__c()] = [0] 928.45/297.09 >= [0] 928.45/297.09 = [l()] 928.45/297.09 928.45/297.09 [a__c()] = [0] 928.45/297.09 >= [0] 928.45/297.09 = [c()] 928.45/297.09 928.45/297.09 [a__b()] = [4] 928.45/297.09 > [0] 928.45/297.09 = [a__c()] 928.45/297.09 928.45/297.09 [a__b()] = [4] 928.45/297.09 >= [4] 928.45/297.09 = [a__d()] 928.45/297.09 928.45/297.09 [a__b()] = [4] 928.45/297.09 >= [4] 928.45/297.09 = [b()] 928.45/297.09 928.45/297.09 [a__k()] = [0] 928.45/297.09 >= [0] 928.45/297.09 = [l()] 928.45/297.09 928.45/297.09 [a__k()] = [0] 928.45/297.09 >= [0] 928.45/297.09 = [m()] 928.45/297.09 928.45/297.09 [a__k()] = [0] 928.45/297.09 >= [0] 928.45/297.09 = [k()] 928.45/297.09 928.45/297.09 [a__d()] = [4] 928.45/297.09 > [0] 928.45/297.09 = [m()] 928.45/297.09 928.45/297.09 [a__d()] = [4] 928.45/297.09 >= [4] 928.45/297.09 = [d()] 928.45/297.09 928.45/297.09 [a__A()] = [1] 928.45/297.09 ? [8] 928.45/297.09 = [a__h(a__f(a__a()), a__f(a__b()))] 928.45/297.09 928.45/297.09 [a__A()] = [1] 928.45/297.09 >= [1] 928.45/297.09 = [A()] 928.45/297.09 928.45/297.09 [a__h(X, X)] = [2] X + [0] 928.45/297.09 >= [0] 928.45/297.09 = [a__g(mark(X), mark(X), a__f(a__k()))] 928.45/297.09 928.45/297.09 [a__h(X1, X2)] = [1] X1 + [1] X2 + [0] 928.45/297.09 ? [1] X1 + [1] X2 + [7] 928.45/297.09 = [h(X1, X2)] 928.45/297.09 928.45/297.09 [a__f(X)] = [1] X + [0] 928.45/297.09 >= [0] 928.45/297.09 = [a__z(mark(X), X)] 928.45/297.09 928.45/297.09 [a__f(X)] = [1] X + [0] 928.45/297.09 >= [1] X + [0] 928.45/297.09 = [f(X)] 928.45/297.09 928.45/297.09 [a__g(X1, X2, X3)] = [1] X1 + [1] X2 + [1] X3 + [0] 928.45/297.09 >= [1] X1 + [1] X2 + [1] X3 + [0] 928.45/297.09 = [g(X1, X2, X3)] 928.45/297.09 928.45/297.09 [a__g(d(), X, X)] = [2] X + [4] 928.45/297.09 > [1] 928.45/297.09 = [a__A()] 928.45/297.09 928.45/297.09 [mark(e())] = [0] 928.45/297.09 ? [4] 928.45/297.09 = [e()] 928.45/297.09 928.45/297.09 [mark(l())] = [0] 928.45/297.09 >= [0] 928.45/297.09 = [l()] 928.45/297.09 928.45/297.09 [mark(m())] = [0] 928.45/297.09 >= [0] 928.45/297.09 = [m()] 928.45/297.09 928.45/297.09 [mark(d())] = [0] 928.45/297.09 ? [4] 928.45/297.09 = [a__d()] 928.45/297.09 928.45/297.09 [mark(A())] = [0] 928.45/297.09 ? [1] 928.45/297.09 = [a__A()] 928.45/297.09 928.45/297.09 [mark(a())] = [0] 928.45/297.09 ? [4] 928.45/297.09 = [a__a()] 928.45/297.09 928.45/297.09 [mark(b())] = [0] 928.45/297.09 ? [4] 928.45/297.09 = [a__b()] 928.45/297.09 928.45/297.09 [mark(c())] = [0] 928.45/297.09 >= [0] 928.45/297.09 = [a__c()] 928.45/297.09 928.45/297.09 [mark(k())] = [0] 928.45/297.09 >= [0] 928.45/297.09 = [a__k()] 928.45/297.09 928.45/297.09 [mark(z(X1, X2))] = [0] 928.45/297.09 >= [0] 928.45/297.09 = [a__z(mark(X1), X2)] 928.45/297.09 928.45/297.09 [mark(f(X))] = [0] 928.45/297.09 >= [0] 928.45/297.09 = [a__f(mark(X))] 928.45/297.09 928.45/297.09 [mark(h(X1, X2))] = [0] 928.45/297.09 >= [0] 928.45/297.09 = [a__h(mark(X1), mark(X2))] 928.45/297.09 928.45/297.09 [mark(g(X1, X2, X3))] = [0] 928.45/297.09 >= [0] 928.45/297.09 = [a__g(mark(X1), mark(X2), mark(X3))] 928.45/297.09 928.45/297.09 [a__z(X1, X2)] = [1] X1 + [0] 928.74/297.10 >= [1] X1 + [0] 928.74/297.10 = [z(X1, X2)] 928.74/297.10 928.74/297.10 [a__z(e(), X)] = [4] 928.74/297.10 > [0] 928.74/297.10 = [mark(X)] 928.74/297.10 928.74/297.10 928.74/297.10 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 928.74/297.10 928.74/297.10 We are left with following problem, upon which TcT provides the 928.74/297.10 certificate MAYBE. 928.74/297.10 928.74/297.10 Strict Trs: 928.74/297.10 { a__c() -> e() 928.74/297.10 , a__b() -> a__d() 928.74/297.10 , a__A() -> a__h(a__f(a__a()), a__f(a__b())) 928.74/297.10 , a__h(X, X) -> a__g(mark(X), mark(X), a__f(a__k())) 928.74/297.10 , a__h(X1, X2) -> h(X1, X2) 928.74/297.10 , a__f(X) -> a__z(mark(X), X) 928.74/297.10 , mark(e()) -> e() 928.74/297.10 , mark(d()) -> a__d() 928.74/297.10 , mark(A()) -> a__A() 928.74/297.10 , mark(a()) -> a__a() 928.74/297.10 , mark(b()) -> a__b() 928.74/297.10 , mark(c()) -> a__c() 928.74/297.10 , mark(k()) -> a__k() 928.74/297.10 , mark(z(X1, X2)) -> a__z(mark(X1), X2) 928.74/297.10 , mark(f(X)) -> a__f(mark(X)) 928.74/297.10 , mark(h(X1, X2)) -> a__h(mark(X1), mark(X2)) 928.74/297.10 , mark(g(X1, X2, X3)) -> a__g(mark(X1), mark(X2), mark(X3)) } 928.74/297.10 Weak Trs: 928.74/297.10 { a__a() -> a__c() 928.74/297.10 , a__a() -> a__d() 928.74/297.10 , a__a() -> a() 928.74/297.10 , a__c() -> l() 928.74/297.10 , a__c() -> c() 928.74/297.10 , a__b() -> a__c() 928.74/297.10 , a__b() -> b() 928.74/297.10 , a__k() -> l() 928.74/297.10 , a__k() -> m() 928.74/297.10 , a__k() -> k() 928.74/297.10 , a__d() -> m() 928.74/297.10 , a__d() -> d() 928.74/297.10 , a__A() -> A() 928.74/297.10 , a__f(X) -> f(X) 928.74/297.10 , a__g(X1, X2, X3) -> g(X1, X2, X3) 928.74/297.10 , a__g(d(), X, X) -> a__A() 928.74/297.10 , mark(l()) -> l() 928.74/297.10 , mark(m()) -> m() 928.74/297.10 , a__z(X1, X2) -> z(X1, X2) 928.74/297.10 , a__z(e(), X) -> mark(X) } 928.74/297.10 Obligation: 928.74/297.10 innermost runtime complexity 928.74/297.10 Answer: 928.74/297.10 MAYBE 928.74/297.10 928.74/297.10 The weightgap principle applies (using the following nonconstant 928.74/297.10 growth matrix-interpretation) 928.74/297.10 928.74/297.10 The following argument positions are usable: 928.74/297.10 Uargs(a__h) = {1, 2}, Uargs(a__f) = {1}, Uargs(a__g) = {1, 2, 3}, 928.74/297.10 Uargs(a__z) = {1} 928.74/297.10 928.74/297.10 TcT has computed the following matrix interpretation satisfying 928.74/297.10 not(EDA) and not(IDA(1)). 928.74/297.10 928.74/297.10 [a__a] = [4] 928.74/297.10 928.74/297.10 [a__c] = [0] 928.74/297.10 928.74/297.10 [a__b] = [6] 928.74/297.10 928.74/297.10 [e] = [4] 928.74/297.10 928.74/297.10 [a__k] = [0] 928.74/297.10 928.74/297.10 [l] = [0] 928.74/297.10 928.74/297.10 [a__d] = [4] 928.74/297.10 928.74/297.10 [m] = [0] 928.74/297.10 928.74/297.10 [a__A] = [1] 928.74/297.10 928.74/297.10 [a__h](x1, x2) = [1] x1 + [1] x2 + [0] 928.74/297.10 928.74/297.10 [a__f](x1) = [1] x1 + [0] 928.74/297.10 928.74/297.10 [a__g](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 928.74/297.10 928.74/297.10 [mark](x1) = [0] 928.74/297.10 928.74/297.10 [d] = [4] 928.74/297.10 928.74/297.10 [a__z](x1, x2) = [1] x1 + [0] 928.74/297.10 928.74/297.10 [A] = [1] 928.74/297.10 928.74/297.10 [a] = [4] 928.74/297.10 928.74/297.10 [b] = [6] 928.74/297.10 928.74/297.10 [c] = [0] 928.74/297.10 928.74/297.10 [k] = [0] 928.74/297.10 928.74/297.10 [z](x1, x2) = [1] x1 + [0] 928.74/297.10 928.74/297.10 [f](x1) = [1] x1 + [0] 928.74/297.10 928.74/297.10 [h](x1, x2) = [1] x1 + [1] x2 + [7] 928.74/297.10 928.74/297.10 [g](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 928.74/297.10 928.74/297.10 The order satisfies the following ordering constraints: 928.74/297.10 928.74/297.10 [a__a()] = [4] 928.74/297.10 > [0] 928.74/297.10 = [a__c()] 928.74/297.10 928.74/297.10 [a__a()] = [4] 928.74/297.10 >= [4] 928.74/297.10 = [a__d()] 928.74/297.10 928.74/297.10 [a__a()] = [4] 928.74/297.10 >= [4] 928.74/297.10 = [a()] 928.74/297.10 928.74/297.10 [a__c()] = [0] 928.74/297.10 ? [4] 928.74/297.10 = [e()] 928.74/297.10 928.74/297.10 [a__c()] = [0] 928.74/297.10 >= [0] 928.74/297.10 = [l()] 928.74/297.10 928.74/297.10 [a__c()] = [0] 928.74/297.10 >= [0] 928.74/297.10 = [c()] 928.74/297.10 928.74/297.10 [a__b()] = [6] 928.74/297.10 > [0] 928.74/297.10 = [a__c()] 928.74/297.10 928.74/297.10 [a__b()] = [6] 928.74/297.10 > [4] 928.74/297.10 = [a__d()] 928.74/297.10 928.74/297.10 [a__b()] = [6] 928.74/297.10 >= [6] 928.74/297.10 = [b()] 928.74/297.10 928.74/297.10 [a__k()] = [0] 928.74/297.10 >= [0] 928.74/297.10 = [l()] 928.74/297.10 928.74/297.10 [a__k()] = [0] 928.74/297.10 >= [0] 928.74/297.10 = [m()] 928.74/297.10 928.74/297.10 [a__k()] = [0] 928.74/297.10 >= [0] 928.74/297.10 = [k()] 928.74/297.10 928.74/297.10 [a__d()] = [4] 928.74/297.10 > [0] 928.74/297.10 = [m()] 928.74/297.10 928.74/297.10 [a__d()] = [4] 928.74/297.10 >= [4] 928.74/297.10 = [d()] 928.74/297.10 928.74/297.10 [a__A()] = [1] 928.74/297.10 ? [10] 928.74/297.10 = [a__h(a__f(a__a()), a__f(a__b()))] 928.74/297.10 928.74/297.10 [a__A()] = [1] 928.74/297.10 >= [1] 928.74/297.10 = [A()] 928.74/297.10 928.74/297.10 [a__h(X, X)] = [2] X + [0] 928.74/297.10 >= [0] 928.74/297.10 = [a__g(mark(X), mark(X), a__f(a__k()))] 928.74/297.10 928.74/297.10 [a__h(X1, X2)] = [1] X1 + [1] X2 + [0] 928.74/297.10 ? [1] X1 + [1] X2 + [7] 928.74/297.10 = [h(X1, X2)] 928.74/297.10 928.74/297.10 [a__f(X)] = [1] X + [0] 928.74/297.10 >= [0] 928.74/297.10 = [a__z(mark(X), X)] 928.74/297.10 928.74/297.10 [a__f(X)] = [1] X + [0] 928.74/297.10 >= [1] X + [0] 928.74/297.10 = [f(X)] 928.74/297.10 928.74/297.10 [a__g(X1, X2, X3)] = [1] X1 + [1] X2 + [1] X3 + [0] 928.74/297.10 >= [1] X1 + [1] X2 + [1] X3 + [0] 928.74/297.10 = [g(X1, X2, X3)] 928.74/297.10 928.74/297.10 [a__g(d(), X, X)] = [2] X + [4] 928.74/297.10 > [1] 928.74/297.10 = [a__A()] 928.74/297.10 928.74/297.10 [mark(e())] = [0] 928.74/297.10 ? [4] 928.74/297.10 = [e()] 928.74/297.10 928.74/297.10 [mark(l())] = [0] 928.74/297.10 >= [0] 928.74/297.10 = [l()] 928.74/297.10 928.74/297.10 [mark(m())] = [0] 928.74/297.10 >= [0] 928.74/297.10 = [m()] 928.74/297.10 928.74/297.10 [mark(d())] = [0] 928.74/297.10 ? [4] 928.74/297.10 = [a__d()] 928.74/297.10 928.74/297.10 [mark(A())] = [0] 928.74/297.10 ? [1] 928.74/297.10 = [a__A()] 928.74/297.10 928.74/297.10 [mark(a())] = [0] 928.74/297.10 ? [4] 928.74/297.10 = [a__a()] 928.74/297.10 928.74/297.10 [mark(b())] = [0] 928.74/297.10 ? [6] 928.74/297.10 = [a__b()] 928.74/297.10 928.74/297.10 [mark(c())] = [0] 928.74/297.10 >= [0] 928.74/297.10 = [a__c()] 928.74/297.10 928.74/297.10 [mark(k())] = [0] 928.74/297.10 >= [0] 928.74/297.10 = [a__k()] 928.74/297.10 928.74/297.10 [mark(z(X1, X2))] = [0] 928.74/297.10 >= [0] 928.74/297.10 = [a__z(mark(X1), X2)] 928.74/297.10 928.74/297.10 [mark(f(X))] = [0] 928.74/297.10 >= [0] 928.74/297.10 = [a__f(mark(X))] 928.74/297.10 928.74/297.10 [mark(h(X1, X2))] = [0] 928.74/297.10 >= [0] 928.74/297.10 = [a__h(mark(X1), mark(X2))] 928.74/297.10 928.74/297.10 [mark(g(X1, X2, X3))] = [0] 928.74/297.10 >= [0] 928.74/297.10 = [a__g(mark(X1), mark(X2), mark(X3))] 928.74/297.10 928.74/297.10 [a__z(X1, X2)] = [1] X1 + [0] 928.74/297.10 >= [1] X1 + [0] 928.74/297.10 = [z(X1, X2)] 928.74/297.10 928.74/297.10 [a__z(e(), X)] = [4] 928.74/297.10 > [0] 928.74/297.10 = [mark(X)] 928.74/297.10 928.74/297.10 928.74/297.10 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 928.74/297.10 928.74/297.10 We are left with following problem, upon which TcT provides the 928.74/297.10 certificate MAYBE. 928.74/297.10 928.74/297.10 Strict Trs: 928.74/297.10 { a__c() -> e() 928.74/297.10 , a__A() -> a__h(a__f(a__a()), a__f(a__b())) 928.74/297.10 , a__h(X, X) -> a__g(mark(X), mark(X), a__f(a__k())) 928.74/297.10 , a__h(X1, X2) -> h(X1, X2) 928.74/297.10 , a__f(X) -> a__z(mark(X), X) 928.74/297.10 , mark(e()) -> e() 928.74/297.10 , mark(d()) -> a__d() 928.74/297.10 , mark(A()) -> a__A() 928.74/297.10 , mark(a()) -> a__a() 928.74/297.10 , mark(b()) -> a__b() 928.74/297.10 , mark(c()) -> a__c() 928.74/297.10 , mark(k()) -> a__k() 928.74/297.10 , mark(z(X1, X2)) -> a__z(mark(X1), X2) 928.74/297.10 , mark(f(X)) -> a__f(mark(X)) 928.74/297.10 , mark(h(X1, X2)) -> a__h(mark(X1), mark(X2)) 928.74/297.10 , mark(g(X1, X2, X3)) -> a__g(mark(X1), mark(X2), mark(X3)) } 928.74/297.10 Weak Trs: 928.74/297.10 { a__a() -> a__c() 928.74/297.10 , a__a() -> a__d() 928.74/297.10 , a__a() -> a() 928.74/297.10 , a__c() -> l() 928.74/297.10 , a__c() -> c() 928.74/297.10 , a__b() -> a__c() 928.74/297.10 , a__b() -> a__d() 928.74/297.10 , a__b() -> b() 928.74/297.10 , a__k() -> l() 928.74/297.10 , a__k() -> m() 928.74/297.10 , a__k() -> k() 928.74/297.10 , a__d() -> m() 928.74/297.10 , a__d() -> d() 928.74/297.10 , a__A() -> A() 928.74/297.10 , a__f(X) -> f(X) 928.74/297.10 , a__g(X1, X2, X3) -> g(X1, X2, X3) 928.74/297.10 , a__g(d(), X, X) -> a__A() 928.74/297.10 , mark(l()) -> l() 928.74/297.10 , mark(m()) -> m() 928.74/297.10 , a__z(X1, X2) -> z(X1, X2) 928.74/297.10 , a__z(e(), X) -> mark(X) } 928.74/297.10 Obligation: 928.74/297.10 innermost runtime complexity 928.74/297.10 Answer: 928.74/297.10 MAYBE 928.74/297.10 928.74/297.10 The weightgap principle applies (using the following nonconstant 928.74/297.10 growth matrix-interpretation) 928.74/297.10 928.74/297.10 The following argument positions are usable: 928.74/297.10 Uargs(a__h) = {1, 2}, Uargs(a__f) = {1}, Uargs(a__g) = {1, 2, 3}, 928.74/297.10 Uargs(a__z) = {1} 928.74/297.10 928.74/297.10 TcT has computed the following matrix interpretation satisfying 928.74/297.10 not(EDA) and not(IDA(1)). 928.74/297.10 928.74/297.10 [a__a] = [4] 928.74/297.10 928.74/297.10 [a__c] = [0] 928.74/297.10 928.74/297.10 [a__b] = [4] 928.74/297.10 928.74/297.10 [e] = [4] 928.74/297.10 928.74/297.10 [a__k] = [0] 928.74/297.10 928.74/297.10 [l] = [0] 928.74/297.10 928.74/297.10 [a__d] = [4] 928.74/297.10 928.74/297.10 [m] = [0] 928.74/297.10 928.74/297.10 [a__A] = [1] 928.74/297.10 928.74/297.10 [a__h](x1, x2) = [1] x1 + [1] x2 + [4] 928.74/297.10 928.74/297.10 [a__f](x1) = [1] x1 + [0] 928.74/297.10 928.74/297.10 [a__g](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 928.74/297.10 928.74/297.10 [mark](x1) = [0] 928.74/297.10 928.74/297.10 [d] = [4] 928.74/297.10 928.74/297.10 [a__z](x1, x2) = [1] x1 + [0] 928.74/297.10 928.74/297.10 [A] = [1] 928.74/297.10 928.74/297.10 [a] = [4] 928.74/297.10 928.74/297.10 [b] = [4] 928.74/297.10 928.74/297.10 [c] = [0] 928.74/297.10 928.74/297.10 [k] = [0] 928.74/297.10 928.74/297.10 [z](x1, x2) = [1] x1 + [0] 928.74/297.10 928.74/297.10 [f](x1) = [1] x1 + [0] 928.74/297.10 928.74/297.10 [h](x1, x2) = [1] x1 + [1] x2 + [3] 928.74/297.10 928.74/297.10 [g](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 928.74/297.10 928.74/297.10 The order satisfies the following ordering constraints: 928.74/297.10 928.74/297.10 [a__a()] = [4] 928.74/297.10 > [0] 928.74/297.10 = [a__c()] 928.74/297.10 928.74/297.10 [a__a()] = [4] 928.74/297.10 >= [4] 928.74/297.10 = [a__d()] 928.74/297.10 928.74/297.10 [a__a()] = [4] 928.74/297.10 >= [4] 928.74/297.10 = [a()] 928.74/297.10 928.74/297.10 [a__c()] = [0] 928.74/297.10 ? [4] 928.74/297.10 = [e()] 928.74/297.10 928.74/297.10 [a__c()] = [0] 928.74/297.10 >= [0] 928.74/297.10 = [l()] 928.74/297.10 928.74/297.10 [a__c()] = [0] 928.74/297.10 >= [0] 928.74/297.10 = [c()] 928.74/297.10 928.74/297.10 [a__b()] = [4] 928.74/297.10 > [0] 928.74/297.10 = [a__c()] 928.74/297.10 928.74/297.10 [a__b()] = [4] 928.74/297.10 >= [4] 928.74/297.10 = [a__d()] 928.74/297.10 928.74/297.11 [a__b()] = [4] 928.74/297.11 >= [4] 928.74/297.11 = [b()] 928.74/297.11 928.74/297.11 [a__k()] = [0] 928.74/297.11 >= [0] 928.74/297.11 = [l()] 928.74/297.11 928.74/297.11 [a__k()] = [0] 928.74/297.11 >= [0] 928.74/297.11 = [m()] 928.74/297.11 928.74/297.11 [a__k()] = [0] 928.74/297.11 >= [0] 928.74/297.11 = [k()] 928.74/297.11 928.74/297.11 [a__d()] = [4] 928.74/297.11 > [0] 928.74/297.11 = [m()] 928.74/297.11 928.74/297.11 [a__d()] = [4] 928.74/297.11 >= [4] 928.74/297.11 = [d()] 928.74/297.11 928.74/297.11 [a__A()] = [1] 928.74/297.11 ? [12] 928.74/297.11 = [a__h(a__f(a__a()), a__f(a__b()))] 928.74/297.11 928.74/297.11 [a__A()] = [1] 928.74/297.11 >= [1] 928.74/297.11 = [A()] 928.74/297.11 928.74/297.11 [a__h(X, X)] = [2] X + [4] 928.74/297.11 > [0] 928.74/297.11 = [a__g(mark(X), mark(X), a__f(a__k()))] 928.74/297.11 928.74/297.11 [a__h(X1, X2)] = [1] X1 + [1] X2 + [4] 928.74/297.11 > [1] X1 + [1] X2 + [3] 928.74/297.11 = [h(X1, X2)] 928.74/297.11 928.74/297.11 [a__f(X)] = [1] X + [0] 928.74/297.11 >= [0] 928.74/297.11 = [a__z(mark(X), X)] 928.74/297.11 928.74/297.11 [a__f(X)] = [1] X + [0] 928.74/297.11 >= [1] X + [0] 928.74/297.11 = [f(X)] 928.74/297.11 928.74/297.11 [a__g(X1, X2, X3)] = [1] X1 + [1] X2 + [1] X3 + [0] 928.74/297.11 >= [1] X1 + [1] X2 + [1] X3 + [0] 928.74/297.11 = [g(X1, X2, X3)] 928.74/297.11 928.74/297.11 [a__g(d(), X, X)] = [2] X + [4] 928.74/297.11 > [1] 928.74/297.11 = [a__A()] 928.74/297.11 928.74/297.11 [mark(e())] = [0] 928.74/297.11 ? [4] 928.74/297.11 = [e()] 928.74/297.11 928.74/297.11 [mark(l())] = [0] 928.74/297.11 >= [0] 928.74/297.11 = [l()] 928.74/297.11 928.74/297.11 [mark(m())] = [0] 928.74/297.11 >= [0] 928.74/297.11 = [m()] 928.74/297.11 928.74/297.11 [mark(d())] = [0] 928.74/297.11 ? [4] 928.74/297.11 = [a__d()] 928.74/297.11 928.74/297.11 [mark(A())] = [0] 928.74/297.11 ? [1] 928.74/297.11 = [a__A()] 928.74/297.11 928.74/297.11 [mark(a())] = [0] 928.74/297.11 ? [4] 928.74/297.11 = [a__a()] 928.74/297.11 928.74/297.11 [mark(b())] = [0] 928.74/297.11 ? [4] 928.74/297.11 = [a__b()] 928.74/297.11 928.74/297.11 [mark(c())] = [0] 928.74/297.11 >= [0] 928.74/297.11 = [a__c()] 928.74/297.11 928.74/297.11 [mark(k())] = [0] 928.74/297.11 >= [0] 928.74/297.11 = [a__k()] 928.74/297.11 928.74/297.11 [mark(z(X1, X2))] = [0] 928.74/297.11 >= [0] 928.74/297.11 = [a__z(mark(X1), X2)] 928.74/297.11 928.74/297.11 [mark(f(X))] = [0] 928.74/297.11 >= [0] 928.74/297.11 = [a__f(mark(X))] 928.74/297.11 928.74/297.11 [mark(h(X1, X2))] = [0] 928.74/297.11 ? [4] 928.74/297.11 = [a__h(mark(X1), mark(X2))] 928.74/297.11 928.74/297.11 [mark(g(X1, X2, X3))] = [0] 928.74/297.11 >= [0] 928.74/297.11 = [a__g(mark(X1), mark(X2), mark(X3))] 928.74/297.11 928.74/297.11 [a__z(X1, X2)] = [1] X1 + [0] 928.74/297.11 >= [1] X1 + [0] 928.74/297.11 = [z(X1, X2)] 928.74/297.11 928.74/297.11 [a__z(e(), X)] = [4] 928.74/297.11 > [0] 928.74/297.11 = [mark(X)] 928.74/297.11 928.74/297.11 928.74/297.11 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 928.74/297.11 928.74/297.11 We are left with following problem, upon which TcT provides the 928.74/297.11 certificate MAYBE. 928.74/297.11 928.74/297.11 Strict Trs: 928.74/297.11 { a__c() -> e() 928.74/297.11 , a__A() -> a__h(a__f(a__a()), a__f(a__b())) 928.74/297.11 , a__f(X) -> a__z(mark(X), X) 928.74/297.11 , mark(e()) -> e() 928.74/297.11 , mark(d()) -> a__d() 928.74/297.11 , mark(A()) -> a__A() 928.74/297.11 , mark(a()) -> a__a() 928.74/297.11 , mark(b()) -> a__b() 928.74/297.11 , mark(c()) -> a__c() 928.74/297.11 , mark(k()) -> a__k() 928.74/297.11 , mark(z(X1, X2)) -> a__z(mark(X1), X2) 928.74/297.11 , mark(f(X)) -> a__f(mark(X)) 928.74/297.11 , mark(h(X1, X2)) -> a__h(mark(X1), mark(X2)) 928.74/297.11 , mark(g(X1, X2, X3)) -> a__g(mark(X1), mark(X2), mark(X3)) } 928.74/297.11 Weak Trs: 928.74/297.11 { a__a() -> a__c() 928.74/297.11 , a__a() -> a__d() 928.74/297.11 , a__a() -> a() 928.74/297.11 , a__c() -> l() 928.74/297.11 , a__c() -> c() 928.74/297.11 , a__b() -> a__c() 928.74/297.11 , a__b() -> a__d() 928.74/297.11 , a__b() -> b() 928.74/297.11 , a__k() -> l() 928.74/297.11 , a__k() -> m() 928.74/297.11 , a__k() -> k() 928.74/297.11 , a__d() -> m() 928.74/297.11 , a__d() -> d() 928.74/297.11 , a__A() -> A() 928.74/297.11 , a__h(X, X) -> a__g(mark(X), mark(X), a__f(a__k())) 928.74/297.11 , a__h(X1, X2) -> h(X1, X2) 928.74/297.11 , a__f(X) -> f(X) 928.74/297.11 , a__g(X1, X2, X3) -> g(X1, X2, X3) 928.74/297.11 , a__g(d(), X, X) -> a__A() 928.74/297.11 , mark(l()) -> l() 928.74/297.11 , mark(m()) -> m() 928.74/297.11 , a__z(X1, X2) -> z(X1, X2) 928.74/297.11 , a__z(e(), X) -> mark(X) } 928.74/297.11 Obligation: 928.74/297.11 innermost runtime complexity 928.74/297.11 Answer: 928.74/297.11 MAYBE 928.74/297.11 928.74/297.11 The weightgap principle applies (using the following nonconstant 928.74/297.11 growth matrix-interpretation) 928.74/297.11 928.74/297.11 The following argument positions are usable: 928.74/297.11 Uargs(a__h) = {1, 2}, Uargs(a__f) = {1}, Uargs(a__g) = {1, 2, 3}, 928.74/297.11 Uargs(a__z) = {1} 928.74/297.11 928.74/297.11 TcT has computed the following matrix interpretation satisfying 928.74/297.11 not(EDA) and not(IDA(1)). 928.74/297.11 928.74/297.11 [a__a] = [5] 928.74/297.11 928.74/297.11 [a__c] = [5] 928.74/297.11 928.74/297.11 [a__b] = [5] 928.74/297.11 928.74/297.11 [e] = [4] 928.74/297.11 928.74/297.11 [a__k] = [0] 928.74/297.11 928.74/297.11 [l] = [0] 928.74/297.11 928.74/297.11 [a__d] = [0] 928.74/297.11 928.74/297.11 [m] = [0] 928.74/297.11 928.74/297.11 [a__A] = [0] 928.74/297.11 928.74/297.11 [a__h](x1, x2) = [1] x1 + [1] x2 + [0] 928.74/297.11 928.74/297.11 [a__f](x1) = [1] x1 + [0] 928.74/297.11 928.74/297.11 [a__g](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 928.74/297.11 928.74/297.11 [mark](x1) = [0] 928.74/297.11 928.74/297.11 [d] = [0] 928.74/297.11 928.74/297.11 [a__z](x1, x2) = [1] x1 + [0] 928.74/297.11 928.74/297.11 [A] = [0] 928.74/297.11 928.74/297.11 [a] = [5] 928.74/297.11 928.74/297.11 [b] = [5] 928.74/297.11 928.74/297.11 [c] = [5] 928.74/297.11 928.74/297.11 [k] = [0] 928.74/297.11 928.74/297.11 [z](x1, x2) = [1] x1 + [0] 928.74/297.11 928.74/297.11 [f](x1) = [1] x1 + [0] 928.74/297.11 928.74/297.11 [h](x1, x2) = [1] x1 + [1] x2 + [0] 928.74/297.11 928.74/297.11 [g](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 928.74/297.11 928.74/297.11 The order satisfies the following ordering constraints: 928.74/297.11 928.74/297.11 [a__a()] = [5] 928.74/297.11 >= [5] 928.74/297.11 = [a__c()] 928.74/297.11 928.74/297.11 [a__a()] = [5] 928.74/297.11 > [0] 928.74/297.11 = [a__d()] 928.74/297.11 928.74/297.11 [a__a()] = [5] 928.74/297.11 >= [5] 928.74/297.11 = [a()] 928.74/297.11 928.74/297.11 [a__c()] = [5] 928.74/297.11 > [4] 928.74/297.11 = [e()] 928.74/297.11 928.74/297.11 [a__c()] = [5] 928.74/297.11 > [0] 928.74/297.11 = [l()] 928.74/297.11 928.74/297.11 [a__c()] = [5] 928.74/297.11 >= [5] 928.74/297.11 = [c()] 928.74/297.11 928.74/297.11 [a__b()] = [5] 928.74/297.11 >= [5] 928.74/297.11 = [a__c()] 928.74/297.11 928.74/297.11 [a__b()] = [5] 928.74/297.11 > [0] 928.74/297.11 = [a__d()] 928.74/297.11 928.74/297.11 [a__b()] = [5] 928.74/297.11 >= [5] 928.74/297.11 = [b()] 928.74/297.11 928.74/297.11 [a__k()] = [0] 928.74/297.11 >= [0] 928.74/297.11 = [l()] 928.74/297.11 928.74/297.11 [a__k()] = [0] 928.74/297.11 >= [0] 928.74/297.11 = [m()] 928.74/297.11 928.74/297.11 [a__k()] = [0] 928.74/297.11 >= [0] 928.74/297.11 = [k()] 928.74/297.11 928.74/297.11 [a__d()] = [0] 928.74/297.11 >= [0] 928.74/297.11 = [m()] 928.74/297.11 928.74/297.11 [a__d()] = [0] 928.74/297.11 >= [0] 928.74/297.11 = [d()] 928.74/297.11 928.74/297.11 [a__A()] = [0] 928.74/297.11 ? [10] 928.74/297.11 = [a__h(a__f(a__a()), a__f(a__b()))] 928.74/297.11 928.74/297.11 [a__A()] = [0] 928.74/297.11 >= [0] 928.74/297.11 = [A()] 928.74/297.11 928.74/297.11 [a__h(X, X)] = [2] X + [0] 928.74/297.11 >= [0] 928.74/297.11 = [a__g(mark(X), mark(X), a__f(a__k()))] 928.74/297.11 928.74/297.11 [a__h(X1, X2)] = [1] X1 + [1] X2 + [0] 928.74/297.11 >= [1] X1 + [1] X2 + [0] 928.74/297.11 = [h(X1, X2)] 928.74/297.11 928.74/297.11 [a__f(X)] = [1] X + [0] 928.74/297.11 >= [0] 928.74/297.11 = [a__z(mark(X), X)] 928.74/297.11 928.74/297.11 [a__f(X)] = [1] X + [0] 928.74/297.11 >= [1] X + [0] 928.74/297.11 = [f(X)] 928.74/297.11 928.74/297.11 [a__g(X1, X2, X3)] = [1] X1 + [1] X2 + [1] X3 + [0] 928.74/297.11 >= [1] X1 + [1] X2 + [1] X3 + [0] 928.74/297.11 = [g(X1, X2, X3)] 928.74/297.11 928.74/297.11 [a__g(d(), X, X)] = [2] X + [0] 928.74/297.11 >= [0] 928.74/297.11 = [a__A()] 928.74/297.11 928.74/297.11 [mark(e())] = [0] 928.74/297.11 ? [4] 928.74/297.11 = [e()] 928.74/297.11 928.74/297.11 [mark(l())] = [0] 928.74/297.11 >= [0] 928.74/297.11 = [l()] 928.74/297.11 928.74/297.11 [mark(m())] = [0] 928.74/297.11 >= [0] 928.74/297.11 = [m()] 928.74/297.11 928.74/297.11 [mark(d())] = [0] 928.74/297.11 >= [0] 928.74/297.11 = [a__d()] 928.74/297.11 928.74/297.11 [mark(A())] = [0] 928.74/297.11 >= [0] 928.74/297.11 = [a__A()] 928.74/297.11 928.74/297.11 [mark(a())] = [0] 928.74/297.11 ? [5] 928.74/297.11 = [a__a()] 928.74/297.11 928.74/297.11 [mark(b())] = [0] 928.74/297.11 ? [5] 928.74/297.11 = [a__b()] 928.74/297.11 928.74/297.11 [mark(c())] = [0] 928.74/297.11 ? [5] 928.74/297.11 = [a__c()] 928.74/297.11 928.74/297.11 [mark(k())] = [0] 928.74/297.11 >= [0] 928.74/297.11 = [a__k()] 928.74/297.11 928.74/297.11 [mark(z(X1, X2))] = [0] 928.74/297.11 >= [0] 928.74/297.11 = [a__z(mark(X1), X2)] 928.74/297.11 928.74/297.11 [mark(f(X))] = [0] 928.74/297.11 >= [0] 928.74/297.11 = [a__f(mark(X))] 928.74/297.11 928.74/297.11 [mark(h(X1, X2))] = [0] 928.74/297.11 >= [0] 928.74/297.11 = [a__h(mark(X1), mark(X2))] 928.74/297.11 928.74/297.11 [mark(g(X1, X2, X3))] = [0] 928.74/297.11 >= [0] 928.74/297.11 = [a__g(mark(X1), mark(X2), mark(X3))] 928.74/297.12 928.74/297.12 [a__z(X1, X2)] = [1] X1 + [0] 928.74/297.12 >= [1] X1 + [0] 928.74/297.12 = [z(X1, X2)] 928.74/297.12 928.74/297.12 [a__z(e(), X)] = [4] 928.74/297.12 > [0] 928.74/297.12 = [mark(X)] 928.74/297.12 928.74/297.12 928.74/297.12 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 928.74/297.12 928.74/297.12 We are left with following problem, upon which TcT provides the 928.74/297.12 certificate MAYBE. 928.74/297.12 928.74/297.12 Strict Trs: 928.74/297.12 { a__A() -> a__h(a__f(a__a()), a__f(a__b())) 928.74/297.12 , a__f(X) -> a__z(mark(X), X) 928.74/297.12 , mark(e()) -> e() 928.74/297.12 , mark(d()) -> a__d() 928.74/297.12 , mark(A()) -> a__A() 928.74/297.12 , mark(a()) -> a__a() 928.74/297.12 , mark(b()) -> a__b() 928.74/297.12 , mark(c()) -> a__c() 928.74/297.12 , mark(k()) -> a__k() 928.74/297.12 , mark(z(X1, X2)) -> a__z(mark(X1), X2) 928.74/297.12 , mark(f(X)) -> a__f(mark(X)) 928.74/297.12 , mark(h(X1, X2)) -> a__h(mark(X1), mark(X2)) 928.74/297.12 , mark(g(X1, X2, X3)) -> a__g(mark(X1), mark(X2), mark(X3)) } 928.74/297.12 Weak Trs: 928.74/297.12 { a__a() -> a__c() 928.74/297.12 , a__a() -> a__d() 928.74/297.12 , a__a() -> a() 928.74/297.12 , a__c() -> e() 928.74/297.12 , a__c() -> l() 928.74/297.12 , a__c() -> c() 928.74/297.12 , a__b() -> a__c() 928.74/297.12 , a__b() -> a__d() 928.74/297.12 , a__b() -> b() 928.74/297.12 , a__k() -> l() 928.74/297.12 , a__k() -> m() 928.74/297.12 , a__k() -> k() 928.74/297.12 , a__d() -> m() 928.74/297.12 , a__d() -> d() 928.74/297.12 , a__A() -> A() 928.74/297.12 , a__h(X, X) -> a__g(mark(X), mark(X), a__f(a__k())) 928.74/297.12 , a__h(X1, X2) -> h(X1, X2) 928.74/297.12 , a__f(X) -> f(X) 928.74/297.12 , a__g(X1, X2, X3) -> g(X1, X2, X3) 928.74/297.12 , a__g(d(), X, X) -> a__A() 928.74/297.12 , mark(l()) -> l() 928.74/297.12 , mark(m()) -> m() 928.74/297.12 , a__z(X1, X2) -> z(X1, X2) 928.74/297.12 , a__z(e(), X) -> mark(X) } 928.74/297.12 Obligation: 928.74/297.12 innermost runtime complexity 928.74/297.12 Answer: 928.74/297.12 MAYBE 928.74/297.12 928.74/297.12 The weightgap principle applies (using the following nonconstant 928.74/297.12 growth matrix-interpretation) 928.74/297.12 928.74/297.12 The following argument positions are usable: 928.74/297.12 Uargs(a__h) = {1, 2}, Uargs(a__f) = {1}, Uargs(a__g) = {1, 2, 3}, 928.74/297.12 Uargs(a__z) = {1} 928.74/297.12 928.74/297.12 TcT has computed the following matrix interpretation satisfying 928.74/297.12 not(EDA) and not(IDA(1)). 928.74/297.12 928.74/297.12 [a__a] = [2] 928.74/297.12 928.74/297.12 [a__c] = [1] 928.74/297.12 928.74/297.12 [a__b] = [1] 928.74/297.12 928.74/297.12 [e] = [1] 928.74/297.12 928.74/297.12 [a__k] = [0] 928.74/297.12 928.74/297.12 [l] = [0] 928.74/297.12 928.74/297.12 [a__d] = [0] 928.74/297.12 928.74/297.12 [m] = [0] 928.74/297.12 928.74/297.12 [a__A] = [0] 928.74/297.12 928.74/297.12 [a__h](x1, x2) = [1] x1 + [1] x2 + [4] 928.74/297.12 928.74/297.12 [a__f](x1) = [1] x1 + [4] 928.74/297.12 928.74/297.12 [a__g](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 928.74/297.12 928.74/297.12 [mark](x1) = [0] 928.74/297.12 928.74/297.12 [d] = [0] 928.74/297.12 928.74/297.12 [a__z](x1, x2) = [1] x1 + [3] 928.74/297.12 928.74/297.12 [A] = [0] 928.74/297.12 928.74/297.12 [a] = [1] 928.74/297.12 928.74/297.12 [b] = [1] 928.74/297.12 928.74/297.12 [c] = [1] 928.74/297.12 928.74/297.12 [k] = [0] 928.74/297.12 928.74/297.12 [z](x1, x2) = [1] x1 + [3] 928.74/297.12 928.74/297.12 [f](x1) = [1] x1 + [4] 928.74/297.12 928.74/297.12 [h](x1, x2) = [1] x1 + [1] x2 + [4] 928.74/297.12 928.74/297.12 [g](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 928.74/297.12 928.74/297.12 The order satisfies the following ordering constraints: 928.74/297.12 928.74/297.12 [a__a()] = [2] 928.74/297.12 > [1] 928.74/297.12 = [a__c()] 928.74/297.12 928.74/297.12 [a__a()] = [2] 928.74/297.12 > [0] 928.74/297.12 = [a__d()] 928.74/297.12 928.74/297.12 [a__a()] = [2] 928.74/297.12 > [1] 928.74/297.12 = [a()] 928.74/297.12 928.74/297.12 [a__c()] = [1] 928.74/297.12 >= [1] 928.74/297.12 = [e()] 928.74/297.12 928.74/297.12 [a__c()] = [1] 928.74/297.12 > [0] 928.74/297.12 = [l()] 928.74/297.12 928.74/297.12 [a__c()] = [1] 928.74/297.12 >= [1] 928.74/297.12 = [c()] 928.74/297.12 928.74/297.12 [a__b()] = [1] 928.74/297.12 >= [1] 928.74/297.12 = [a__c()] 928.74/297.12 928.74/297.12 [a__b()] = [1] 928.74/297.12 > [0] 928.74/297.12 = [a__d()] 928.74/297.12 928.74/297.12 [a__b()] = [1] 928.74/297.12 >= [1] 928.74/297.12 = [b()] 928.74/297.12 928.74/297.12 [a__k()] = [0] 928.74/297.12 >= [0] 928.74/297.12 = [l()] 928.74/297.12 928.74/297.12 [a__k()] = [0] 928.74/297.12 >= [0] 928.74/297.12 = [m()] 928.74/297.12 928.74/297.12 [a__k()] = [0] 928.74/297.12 >= [0] 928.74/297.12 = [k()] 928.74/297.12 928.74/297.12 [a__d()] = [0] 928.74/297.12 >= [0] 928.74/297.12 = [m()] 928.74/297.12 928.74/297.12 [a__d()] = [0] 928.74/297.12 >= [0] 928.74/297.12 = [d()] 928.74/297.12 928.74/297.12 [a__A()] = [0] 928.74/297.12 ? [15] 928.74/297.12 = [a__h(a__f(a__a()), a__f(a__b()))] 928.74/297.12 928.74/297.12 [a__A()] = [0] 928.74/297.12 >= [0] 928.74/297.12 = [A()] 928.74/297.12 928.74/297.12 [a__h(X, X)] = [2] X + [4] 928.74/297.12 >= [4] 928.74/297.12 = [a__g(mark(X), mark(X), a__f(a__k()))] 928.74/297.12 928.74/297.12 [a__h(X1, X2)] = [1] X1 + [1] X2 + [4] 928.74/297.12 >= [1] X1 + [1] X2 + [4] 928.74/297.12 = [h(X1, X2)] 928.74/297.12 928.74/297.12 [a__f(X)] = [1] X + [4] 928.74/297.12 > [3] 928.74/297.12 = [a__z(mark(X), X)] 928.74/297.12 928.74/297.12 [a__f(X)] = [1] X + [4] 928.74/297.12 >= [1] X + [4] 928.74/297.12 = [f(X)] 928.74/297.12 928.74/297.12 [a__g(X1, X2, X3)] = [1] X1 + [1] X2 + [1] X3 + [0] 928.74/297.12 >= [1] X1 + [1] X2 + [1] X3 + [0] 928.74/297.12 = [g(X1, X2, X3)] 928.74/297.12 928.74/297.12 [a__g(d(), X, X)] = [2] X + [0] 928.74/297.12 >= [0] 928.74/297.12 = [a__A()] 928.74/297.12 928.74/297.12 [mark(e())] = [0] 928.74/297.12 ? [1] 928.74/297.12 = [e()] 928.74/297.12 928.74/297.12 [mark(l())] = [0] 928.74/297.12 >= [0] 928.74/297.12 = [l()] 928.74/297.12 928.74/297.12 [mark(m())] = [0] 928.74/297.12 >= [0] 928.74/297.12 = [m()] 928.74/297.12 928.74/297.12 [mark(d())] = [0] 928.74/297.12 >= [0] 928.74/297.12 = [a__d()] 928.74/297.12 928.74/297.12 [mark(A())] = [0] 928.74/297.12 >= [0] 928.74/297.12 = [a__A()] 928.74/297.12 928.74/297.12 [mark(a())] = [0] 928.74/297.12 ? [2] 928.74/297.12 = [a__a()] 928.74/297.12 928.74/297.12 [mark(b())] = [0] 928.74/297.12 ? [1] 928.74/297.12 = [a__b()] 928.74/297.12 928.74/297.12 [mark(c())] = [0] 928.74/297.12 ? [1] 928.74/297.12 = [a__c()] 928.74/297.12 928.74/297.12 [mark(k())] = [0] 928.74/297.12 >= [0] 928.74/297.12 = [a__k()] 928.74/297.12 928.74/297.12 [mark(z(X1, X2))] = [0] 928.74/297.12 ? [3] 928.74/297.12 = [a__z(mark(X1), X2)] 928.74/297.12 928.74/297.12 [mark(f(X))] = [0] 928.74/297.12 ? [4] 928.74/297.12 = [a__f(mark(X))] 928.74/297.12 928.74/297.12 [mark(h(X1, X2))] = [0] 928.74/297.12 ? [4] 928.74/297.12 = [a__h(mark(X1), mark(X2))] 928.74/297.12 928.74/297.12 [mark(g(X1, X2, X3))] = [0] 928.74/297.12 >= [0] 928.74/297.13 = [a__g(mark(X1), mark(X2), mark(X3))] 928.74/297.13 928.74/297.13 [a__z(X1, X2)] = [1] X1 + [3] 928.74/297.13 >= [1] X1 + [3] 928.74/297.13 = [z(X1, X2)] 928.74/297.13 928.74/297.13 [a__z(e(), X)] = [4] 928.74/297.13 > [0] 928.74/297.13 = [mark(X)] 928.74/297.13 928.74/297.13 928.74/297.13 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 928.74/297.13 928.74/297.13 We are left with following problem, upon which TcT provides the 928.74/297.13 certificate MAYBE. 928.74/297.13 928.74/297.13 Strict Trs: 928.74/297.13 { a__A() -> a__h(a__f(a__a()), a__f(a__b())) 928.74/297.13 , mark(e()) -> e() 928.74/297.13 , mark(d()) -> a__d() 928.74/297.13 , mark(A()) -> a__A() 928.74/297.13 , mark(a()) -> a__a() 928.74/297.13 , mark(b()) -> a__b() 928.74/297.13 , mark(c()) -> a__c() 928.74/297.13 , mark(k()) -> a__k() 928.74/297.13 , mark(z(X1, X2)) -> a__z(mark(X1), X2) 928.74/297.13 , mark(f(X)) -> a__f(mark(X)) 928.74/297.13 , mark(h(X1, X2)) -> a__h(mark(X1), mark(X2)) 928.74/297.13 , mark(g(X1, X2, X3)) -> a__g(mark(X1), mark(X2), mark(X3)) } 928.74/297.13 Weak Trs: 928.74/297.13 { a__a() -> a__c() 928.74/297.13 , a__a() -> a__d() 928.74/297.13 , a__a() -> a() 928.74/297.13 , a__c() -> e() 928.74/297.13 , a__c() -> l() 928.74/297.13 , a__c() -> c() 928.74/297.13 , a__b() -> a__c() 928.74/297.13 , a__b() -> a__d() 928.74/297.13 , a__b() -> b() 928.74/297.13 , a__k() -> l() 928.74/297.13 , a__k() -> m() 928.74/297.13 , a__k() -> k() 928.74/297.13 , a__d() -> m() 928.74/297.13 , a__d() -> d() 928.74/297.13 , a__A() -> A() 928.74/297.13 , a__h(X, X) -> a__g(mark(X), mark(X), a__f(a__k())) 928.74/297.13 , a__h(X1, X2) -> h(X1, X2) 928.74/297.13 , a__f(X) -> a__z(mark(X), X) 928.74/297.13 , a__f(X) -> f(X) 928.74/297.13 , a__g(X1, X2, X3) -> g(X1, X2, X3) 928.74/297.13 , a__g(d(), X, X) -> a__A() 928.74/297.13 , mark(l()) -> l() 928.74/297.13 , mark(m()) -> m() 928.74/297.13 , a__z(X1, X2) -> z(X1, X2) 928.74/297.13 , a__z(e(), X) -> mark(X) } 928.74/297.13 Obligation: 928.74/297.13 innermost runtime complexity 928.74/297.13 Answer: 928.74/297.13 MAYBE 928.74/297.13 928.74/297.13 The weightgap principle applies (using the following nonconstant 928.74/297.13 growth matrix-interpretation) 928.74/297.13 928.74/297.13 The following argument positions are usable: 928.74/297.13 Uargs(a__h) = {1, 2}, Uargs(a__f) = {1}, Uargs(a__g) = {1, 2, 3}, 928.74/297.13 Uargs(a__z) = {1} 928.74/297.13 928.74/297.13 TcT has computed the following matrix interpretation satisfying 928.74/297.13 not(EDA) and not(IDA(1)). 928.74/297.13 928.74/297.13 [a__a] = [0] 928.74/297.13 928.74/297.13 [a__c] = [0] 928.74/297.13 928.74/297.13 [a__b] = [0] 928.74/297.13 928.74/297.13 [e] = [0] 928.74/297.13 928.74/297.13 [a__k] = [0] 928.74/297.13 928.74/297.13 [l] = [0] 928.74/297.13 928.74/297.13 [a__d] = [0] 928.74/297.13 928.74/297.13 [m] = [0] 928.74/297.13 928.74/297.13 [a__A] = [0] 928.74/297.13 928.74/297.13 [a__h](x1, x2) = [1] x1 + [1] x2 + [7] 928.74/297.13 928.74/297.13 [a__f](x1) = [1] x1 + [4] 928.74/297.13 928.74/297.13 [a__g](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [1] 928.74/297.13 928.74/297.13 [mark](x1) = [1] 928.74/297.13 928.74/297.13 [d] = [0] 928.74/297.13 928.74/297.13 [a__z](x1, x2) = [1] x1 + [2] 928.74/297.13 928.74/297.13 [A] = [0] 928.74/297.13 928.74/297.13 [a] = [0] 928.74/297.13 928.74/297.13 [b] = [0] 928.74/297.13 928.74/297.13 [c] = [0] 928.74/297.13 928.74/297.13 [k] = [0] 928.74/297.13 928.74/297.13 [z](x1, x2) = [1] x1 + [1] 928.74/297.13 928.74/297.13 [f](x1) = [1] x1 + [4] 928.74/297.13 928.74/297.13 [h](x1, x2) = [1] x1 + [1] x2 + [7] 928.74/297.13 928.74/297.13 [g](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [1] 928.74/297.13 928.74/297.13 The order satisfies the following ordering constraints: 928.74/297.13 928.74/297.13 [a__a()] = [0] 928.74/297.13 >= [0] 928.74/297.13 = [a__c()] 928.74/297.13 928.74/297.13 [a__a()] = [0] 928.74/297.13 >= [0] 928.74/297.13 = [a__d()] 928.74/297.13 928.74/297.13 [a__a()] = [0] 928.74/297.13 >= [0] 928.74/297.13 = [a()] 928.74/297.13 928.74/297.13 [a__c()] = [0] 928.74/297.13 >= [0] 928.74/297.13 = [e()] 928.74/297.13 928.74/297.13 [a__c()] = [0] 928.74/297.13 >= [0] 928.74/297.13 = [l()] 928.74/297.13 928.74/297.13 [a__c()] = [0] 928.74/297.13 >= [0] 928.74/297.13 = [c()] 928.74/297.13 928.74/297.13 [a__b()] = [0] 928.74/297.13 >= [0] 928.74/297.13 = [a__c()] 928.74/297.13 928.74/297.13 [a__b()] = [0] 928.74/297.13 >= [0] 928.74/297.13 = [a__d()] 928.74/297.13 928.74/297.13 [a__b()] = [0] 928.74/297.13 >= [0] 928.74/297.13 = [b()] 928.74/297.13 928.74/297.13 [a__k()] = [0] 928.74/297.13 >= [0] 928.74/297.13 = [l()] 928.74/297.13 928.74/297.13 [a__k()] = [0] 928.74/297.13 >= [0] 928.74/297.13 = [m()] 928.74/297.13 928.74/297.13 [a__k()] = [0] 928.74/297.13 >= [0] 928.74/297.13 = [k()] 928.74/297.13 928.74/297.13 [a__d()] = [0] 928.74/297.13 >= [0] 928.74/297.13 = [m()] 928.74/297.13 928.74/297.13 [a__d()] = [0] 928.74/297.13 >= [0] 928.74/297.13 = [d()] 928.74/297.13 928.74/297.13 [a__A()] = [0] 928.74/297.13 ? [15] 928.74/297.13 = [a__h(a__f(a__a()), a__f(a__b()))] 928.74/297.13 928.74/297.13 [a__A()] = [0] 928.74/297.13 >= [0] 928.74/297.13 = [A()] 928.74/297.13 928.74/297.13 [a__h(X, X)] = [2] X + [7] 928.74/297.13 >= [7] 928.74/297.13 = [a__g(mark(X), mark(X), a__f(a__k()))] 928.74/297.13 928.74/297.13 [a__h(X1, X2)] = [1] X1 + [1] X2 + [7] 928.74/297.13 >= [1] X1 + [1] X2 + [7] 928.74/297.13 = [h(X1, X2)] 928.74/297.13 928.74/297.13 [a__f(X)] = [1] X + [4] 928.74/297.13 > [3] 928.74/297.13 = [a__z(mark(X), X)] 928.74/297.13 928.74/297.13 [a__f(X)] = [1] X + [4] 928.74/297.13 >= [1] X + [4] 928.74/297.13 = [f(X)] 928.74/297.13 928.74/297.13 [a__g(X1, X2, X3)] = [1] X1 + [1] X2 + [1] X3 + [1] 928.74/297.13 >= [1] X1 + [1] X2 + [1] X3 + [1] 928.74/297.13 = [g(X1, X2, X3)] 928.74/297.13 928.74/297.13 [a__g(d(), X, X)] = [2] X + [1] 928.74/297.13 > [0] 928.74/297.13 = [a__A()] 928.74/297.13 928.74/297.13 [mark(e())] = [1] 928.74/297.13 > [0] 928.74/297.13 = [e()] 928.74/297.13 928.74/297.13 [mark(l())] = [1] 928.74/297.13 > [0] 928.74/297.13 = [l()] 928.74/297.13 928.74/297.13 [mark(m())] = [1] 928.74/297.13 > [0] 928.74/297.13 = [m()] 928.74/297.13 928.74/297.13 [mark(d())] = [1] 928.74/297.13 > [0] 928.74/297.13 = [a__d()] 928.74/297.13 928.74/297.13 [mark(A())] = [1] 928.74/297.13 > [0] 928.74/297.13 = [a__A()] 928.74/297.13 928.74/297.13 [mark(a())] = [1] 928.74/297.13 > [0] 928.74/297.13 = [a__a()] 928.74/297.13 928.74/297.13 [mark(b())] = [1] 928.74/297.13 > [0] 928.74/297.13 = [a__b()] 928.74/297.13 928.74/297.13 [mark(c())] = [1] 928.74/297.13 > [0] 928.74/297.13 = [a__c()] 928.74/297.13 928.74/297.13 [mark(k())] = [1] 928.74/297.13 > [0] 928.74/297.13 = [a__k()] 928.74/297.13 928.74/297.13 [mark(z(X1, X2))] = [1] 928.74/297.13 ? [3] 928.74/297.13 = [a__z(mark(X1), X2)] 928.74/297.13 928.74/297.13 [mark(f(X))] = [1] 928.74/297.13 ? [5] 928.74/297.13 = [a__f(mark(X))] 928.74/297.13 928.74/297.13 [mark(h(X1, X2))] = [1] 928.74/297.13 ? [9] 928.74/297.13 = [a__h(mark(X1), mark(X2))] 928.74/297.13 928.74/297.13 [mark(g(X1, X2, X3))] = [1] 928.74/297.13 ? [4] 928.74/297.13 = [a__g(mark(X1), mark(X2), mark(X3))] 928.74/297.13 928.74/297.13 [a__z(X1, X2)] = [1] X1 + [2] 928.74/297.13 > [1] X1 + [1] 928.74/297.13 = [z(X1, X2)] 928.74/297.13 928.74/297.13 [a__z(e(), X)] = [2] 928.74/297.13 > [1] 928.74/297.13 = [mark(X)] 928.74/297.13 928.74/297.13 928.74/297.13 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 928.74/297.13 928.74/297.13 We are left with following problem, upon which TcT provides the 928.74/297.13 certificate MAYBE. 928.74/297.13 928.74/297.13 Strict Trs: 928.74/297.13 { a__A() -> a__h(a__f(a__a()), a__f(a__b())) 928.74/297.13 , mark(z(X1, X2)) -> a__z(mark(X1), X2) 928.74/297.13 , mark(f(X)) -> a__f(mark(X)) 928.74/297.13 , mark(h(X1, X2)) -> a__h(mark(X1), mark(X2)) 928.74/297.13 , mark(g(X1, X2, X3)) -> a__g(mark(X1), mark(X2), mark(X3)) } 928.74/297.13 Weak Trs: 928.74/297.13 { a__a() -> a__c() 928.74/297.13 , a__a() -> a__d() 928.74/297.13 , a__a() -> a() 928.74/297.13 , a__c() -> e() 928.74/297.13 , a__c() -> l() 928.74/297.13 , a__c() -> c() 928.74/297.13 , a__b() -> a__c() 928.74/297.13 , a__b() -> a__d() 928.74/297.13 , a__b() -> b() 928.74/297.13 , a__k() -> l() 928.74/297.13 , a__k() -> m() 928.74/297.13 , a__k() -> k() 928.74/297.13 , a__d() -> m() 928.74/297.13 , a__d() -> d() 928.74/297.13 , a__A() -> A() 928.74/297.13 , a__h(X, X) -> a__g(mark(X), mark(X), a__f(a__k())) 928.74/297.13 , a__h(X1, X2) -> h(X1, X2) 928.74/297.13 , a__f(X) -> a__z(mark(X), X) 928.74/297.13 , a__f(X) -> f(X) 928.74/297.13 , a__g(X1, X2, X3) -> g(X1, X2, X3) 928.74/297.13 , a__g(d(), X, X) -> a__A() 928.74/297.13 , mark(e()) -> e() 928.74/297.13 , mark(l()) -> l() 928.74/297.13 , mark(m()) -> m() 928.74/297.13 , mark(d()) -> a__d() 928.74/297.13 , mark(A()) -> a__A() 928.74/297.13 , mark(a()) -> a__a() 928.74/297.13 , mark(b()) -> a__b() 928.74/297.13 , mark(c()) -> a__c() 928.74/297.13 , mark(k()) -> a__k() 928.74/297.13 , a__z(X1, X2) -> z(X1, X2) 928.74/297.13 , a__z(e(), X) -> mark(X) } 928.74/297.13 Obligation: 928.74/297.13 innermost runtime complexity 928.74/297.13 Answer: 928.74/297.13 MAYBE 928.74/297.13 928.74/297.13 None of the processors succeeded. 928.74/297.13 928.74/297.13 Details of failed attempt(s): 928.74/297.13 ----------------------------- 928.74/297.13 1) 'empty' failed due to the following reason: 928.74/297.13 928.74/297.13 Empty strict component of the problem is NOT empty. 928.74/297.13 928.74/297.13 2) 'With Problem ...' failed due to the following reason: 928.74/297.13 928.74/297.13 None of the processors succeeded. 928.74/297.13 928.74/297.13 Details of failed attempt(s): 928.74/297.13 ----------------------------- 928.74/297.13 1) 'empty' failed due to the following reason: 928.74/297.13 928.74/297.13 Empty strict component of the problem is NOT empty. 928.74/297.13 928.74/297.13 2) 'Fastest' failed due to the following reason: 928.74/297.13 928.74/297.13 None of the processors succeeded. 928.74/297.13 928.74/297.13 Details of failed attempt(s): 928.74/297.13 ----------------------------- 928.74/297.13 1) 'With Problem ...' failed due to the following reason: 928.74/297.13 928.74/297.13 None of the processors succeeded. 928.74/297.13 928.74/297.13 Details of failed attempt(s): 928.74/297.13 ----------------------------- 928.74/297.13 1) 'empty' failed due to the following reason: 928.74/297.13 928.74/297.13 Empty strict component of the problem is NOT empty. 928.74/297.13 928.74/297.13 2) 'With Problem ...' failed due to the following reason: 928.74/297.13 928.74/297.13 None of the processors succeeded. 928.74/297.13 928.74/297.13 Details of failed attempt(s): 928.74/297.13 ----------------------------- 928.74/297.13 1) 'empty' failed due to the following reason: 928.74/297.13 928.74/297.13 Empty strict component of the problem is NOT empty. 928.74/297.13 928.74/297.13 2) 'With Problem ...' failed due to the following reason: 928.74/297.13 928.74/297.13 None of the processors succeeded. 928.74/297.13 928.74/297.13 Details of failed attempt(s): 928.74/297.13 ----------------------------- 928.74/297.13 1) 'empty' failed due to the following reason: 928.74/297.13 928.74/297.13 Empty strict component of the problem is NOT empty. 928.74/297.13 928.74/297.13 2) 'With Problem ...' failed due to the following reason: 928.74/297.13 928.74/297.13 Empty strict component of the problem is NOT empty. 928.74/297.13 928.74/297.13 928.74/297.13 928.74/297.13 928.74/297.13 2) 'With Problem ...' failed due to the following reason: 928.74/297.13 928.74/297.13 None of the processors succeeded. 928.74/297.13 928.74/297.13 Details of failed attempt(s): 928.74/297.13 ----------------------------- 928.74/297.13 1) 'empty' failed due to the following reason: 928.74/297.13 928.74/297.13 Empty strict component of the problem is NOT empty. 928.74/297.13 928.74/297.13 2) 'With Problem ...' failed due to the following reason: 928.74/297.13 928.74/297.13 Empty strict component of the problem is NOT empty. 928.74/297.13 928.74/297.13 928.74/297.13 928.74/297.13 928.74/297.13 928.74/297.13 2) 'Best' failed due to the following reason: 928.74/297.13 928.74/297.13 None of the processors succeeded. 928.74/297.13 928.74/297.13 Details of failed attempt(s): 928.74/297.13 ----------------------------- 928.74/297.13 1) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 928.74/297.13 to the following reason: 928.74/297.13 928.74/297.13 The input cannot be shown compatible 928.74/297.13 928.74/297.13 2) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 928.74/297.13 following reason: 928.74/297.13 928.74/297.13 The input cannot be shown compatible 928.74/297.13 928.74/297.13 928.74/297.13 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 928.74/297.13 failed due to the following reason: 928.74/297.13 928.74/297.13 None of the processors succeeded. 928.74/297.13 928.74/297.13 Details of failed attempt(s): 928.74/297.13 ----------------------------- 928.74/297.13 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 928.74/297.13 failed due to the following reason: 928.74/297.13 928.74/297.13 match-boundness of the problem could not be verified. 928.74/297.13 928.74/297.13 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 928.74/297.13 failed due to the following reason: 928.74/297.13 928.74/297.13 match-boundness of the problem could not be verified. 928.74/297.13 928.74/297.13 928.74/297.13 928.74/297.13 928.74/297.13 928.74/297.13 Arrrr.. 929.61/297.99 EOF