MAYBE 857.20/297.03 MAYBE 857.20/297.03 857.20/297.03 We are left with following problem, upon which TcT provides the 857.20/297.03 certificate MAYBE. 857.20/297.03 857.20/297.03 Strict Trs: 857.20/297.03 { a__and(X1, X2) -> and(X1, X2) 857.20/297.03 , a__and(tt(), X) -> mark(X) 857.20/297.03 , mark(tt()) -> tt() 857.20/297.03 , mark(0()) -> 0() 857.20/297.03 , mark(s(X)) -> s(mark(X)) 857.20/297.03 , mark(and(X1, X2)) -> a__and(mark(X1), X2) 857.20/297.03 , mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) 857.20/297.03 , a__plus(X1, X2) -> plus(X1, X2) 857.20/297.03 , a__plus(N, 0()) -> mark(N) 857.20/297.03 , a__plus(N, s(M)) -> s(a__plus(mark(N), mark(M))) } 857.20/297.03 Obligation: 857.20/297.03 innermost runtime complexity 857.20/297.03 Answer: 857.20/297.03 MAYBE 857.20/297.03 857.20/297.03 None of the processors succeeded. 857.20/297.03 857.20/297.03 Details of failed attempt(s): 857.20/297.03 ----------------------------- 857.20/297.03 1) 'empty' failed due to the following reason: 857.20/297.03 857.20/297.03 Empty strict component of the problem is NOT empty. 857.20/297.03 857.20/297.03 2) 'Best' failed due to the following reason: 857.20/297.03 857.20/297.03 None of the processors succeeded. 857.20/297.03 857.20/297.03 Details of failed attempt(s): 857.20/297.03 ----------------------------- 857.20/297.03 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 857.20/297.03 following reason: 857.20/297.03 857.20/297.03 Computation stopped due to timeout after 297.0 seconds. 857.20/297.03 857.20/297.03 2) 'Best' failed due to the following reason: 857.20/297.03 857.20/297.03 None of the processors succeeded. 857.20/297.03 857.20/297.03 Details of failed attempt(s): 857.20/297.03 ----------------------------- 857.20/297.03 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 857.20/297.03 seconds)' failed due to the following reason: 857.20/297.03 857.20/297.03 The weightgap principle applies (using the following nonconstant 857.20/297.03 growth matrix-interpretation) 857.20/297.03 857.20/297.03 The following argument positions are usable: 857.20/297.03 Uargs(a__and) = {1}, Uargs(a__plus) = {1, 2}, Uargs(s) = {1} 857.20/297.03 857.20/297.03 TcT has computed the following matrix interpretation satisfying 857.20/297.03 not(EDA) and not(IDA(1)). 857.20/297.03 857.20/297.03 [a__and](x1, x2) = [1] x1 + [1] 857.20/297.03 857.20/297.03 [tt] = [0] 857.20/297.03 857.20/297.03 [mark](x1) = [0] 857.20/297.03 857.20/297.03 [a__plus](x1, x2) = [1] x1 + [1] x2 + [0] 857.20/297.03 857.20/297.03 [0] = [0] 857.20/297.03 857.20/297.03 [s](x1) = [1] x1 + [0] 857.20/297.03 857.20/297.03 [and](x1, x2) = [1] x1 + [0] 857.20/297.03 857.20/297.03 [plus](x1, x2) = [1] x1 + [1] x2 + [7] 857.20/297.03 857.20/297.03 The order satisfies the following ordering constraints: 857.20/297.03 857.20/297.03 [a__and(X1, X2)] = [1] X1 + [1] 857.20/297.03 > [1] X1 + [0] 857.20/297.03 = [and(X1, X2)] 857.20/297.03 857.20/297.03 [a__and(tt(), X)] = [1] 857.20/297.03 > [0] 857.20/297.03 = [mark(X)] 857.20/297.03 857.20/297.03 [mark(tt())] = [0] 857.20/297.03 >= [0] 857.20/297.03 = [tt()] 857.20/297.03 857.20/297.03 [mark(0())] = [0] 857.20/297.03 >= [0] 857.20/297.03 = [0()] 857.20/297.03 857.20/297.03 [mark(s(X))] = [0] 857.20/297.03 >= [0] 857.20/297.03 = [s(mark(X))] 857.20/297.03 857.20/297.03 [mark(and(X1, X2))] = [0] 857.20/297.03 ? [1] 857.20/297.03 = [a__and(mark(X1), X2)] 857.20/297.03 857.20/297.03 [mark(plus(X1, X2))] = [0] 857.20/297.03 >= [0] 857.20/297.03 = [a__plus(mark(X1), mark(X2))] 857.20/297.03 857.20/297.03 [a__plus(X1, X2)] = [1] X1 + [1] X2 + [0] 857.20/297.03 ? [1] X1 + [1] X2 + [7] 857.20/297.03 = [plus(X1, X2)] 857.20/297.03 857.20/297.03 [a__plus(N, 0())] = [1] N + [0] 857.20/297.03 >= [0] 857.20/297.03 = [mark(N)] 857.20/297.03 857.20/297.03 [a__plus(N, s(M))] = [1] N + [1] M + [0] 857.20/297.03 >= [0] 857.20/297.03 = [s(a__plus(mark(N), mark(M)))] 857.20/297.03 857.20/297.03 857.20/297.03 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 857.20/297.03 857.20/297.03 We are left with following problem, upon which TcT provides the 857.20/297.03 certificate MAYBE. 857.20/297.03 857.20/297.03 Strict Trs: 857.20/297.03 { mark(tt()) -> tt() 857.20/297.03 , mark(0()) -> 0() 857.20/297.03 , mark(s(X)) -> s(mark(X)) 857.20/297.03 , mark(and(X1, X2)) -> a__and(mark(X1), X2) 857.20/297.03 , mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) 857.20/297.03 , a__plus(X1, X2) -> plus(X1, X2) 857.20/297.03 , a__plus(N, 0()) -> mark(N) 857.20/297.03 , a__plus(N, s(M)) -> s(a__plus(mark(N), mark(M))) } 857.20/297.03 Weak Trs: 857.20/297.03 { a__and(X1, X2) -> and(X1, X2) 857.20/297.03 , a__and(tt(), X) -> mark(X) } 857.20/297.03 Obligation: 857.20/297.03 innermost runtime complexity 857.20/297.03 Answer: 857.20/297.03 MAYBE 857.20/297.03 857.20/297.03 The weightgap principle applies (using the following nonconstant 857.20/297.03 growth matrix-interpretation) 857.20/297.03 857.20/297.03 The following argument positions are usable: 857.20/297.03 Uargs(a__and) = {1}, Uargs(a__plus) = {1, 2}, Uargs(s) = {1} 857.20/297.03 857.20/297.03 TcT has computed the following matrix interpretation satisfying 857.20/297.03 not(EDA) and not(IDA(1)). 857.20/297.03 857.20/297.03 [a__and](x1, x2) = [1] x1 + [1] x2 + [4] 857.20/297.03 857.20/297.03 [tt] = [0] 857.20/297.03 857.20/297.03 [mark](x1) = [1] x1 + [0] 857.20/297.03 857.20/297.03 [a__plus](x1, x2) = [1] x1 + [1] x2 + [0] 857.20/297.03 857.20/297.03 [0] = [0] 857.20/297.03 857.20/297.03 [s](x1) = [1] x1 + [0] 857.20/297.03 857.20/297.03 [and](x1, x2) = [1] x1 + [1] x2 + [0] 857.20/297.03 857.20/297.03 [plus](x1, x2) = [1] x1 + [1] x2 + [4] 857.20/297.03 857.20/297.03 The order satisfies the following ordering constraints: 857.20/297.03 857.20/297.03 [a__and(X1, X2)] = [1] X1 + [1] X2 + [4] 857.20/297.03 > [1] X1 + [1] X2 + [0] 857.20/297.03 = [and(X1, X2)] 857.20/297.03 857.20/297.03 [a__and(tt(), X)] = [1] X + [4] 857.20/297.03 > [1] X + [0] 857.20/297.03 = [mark(X)] 857.20/297.03 857.20/297.03 [mark(tt())] = [0] 857.20/297.03 >= [0] 857.20/297.03 = [tt()] 857.20/297.03 857.20/297.03 [mark(0())] = [0] 857.20/297.03 >= [0] 857.20/297.03 = [0()] 857.20/297.03 857.20/297.03 [mark(s(X))] = [1] X + [0] 857.20/297.03 >= [1] X + [0] 857.20/297.03 = [s(mark(X))] 857.20/297.03 857.20/297.03 [mark(and(X1, X2))] = [1] X1 + [1] X2 + [0] 857.20/297.03 ? [1] X1 + [1] X2 + [4] 857.20/297.03 = [a__and(mark(X1), X2)] 857.20/297.03 857.20/297.03 [mark(plus(X1, X2))] = [1] X1 + [1] X2 + [4] 857.20/297.03 > [1] X1 + [1] X2 + [0] 857.20/297.03 = [a__plus(mark(X1), mark(X2))] 857.20/297.03 857.20/297.03 [a__plus(X1, X2)] = [1] X1 + [1] X2 + [0] 857.20/297.03 ? [1] X1 + [1] X2 + [4] 857.20/297.03 = [plus(X1, X2)] 857.20/297.03 857.20/297.03 [a__plus(N, 0())] = [1] N + [0] 857.20/297.03 >= [1] N + [0] 857.20/297.03 = [mark(N)] 857.20/297.03 857.20/297.03 [a__plus(N, s(M))] = [1] N + [1] M + [0] 857.20/297.03 >= [1] N + [1] M + [0] 857.20/297.03 = [s(a__plus(mark(N), mark(M)))] 857.20/297.03 857.20/297.03 857.20/297.03 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 857.20/297.03 857.20/297.03 We are left with following problem, upon which TcT provides the 857.20/297.03 certificate MAYBE. 857.20/297.03 857.20/297.03 Strict Trs: 857.20/297.03 { mark(tt()) -> tt() 857.20/297.03 , mark(0()) -> 0() 857.20/297.03 , mark(s(X)) -> s(mark(X)) 857.20/297.03 , mark(and(X1, X2)) -> a__and(mark(X1), X2) 857.20/297.03 , a__plus(X1, X2) -> plus(X1, X2) 857.20/297.03 , a__plus(N, 0()) -> mark(N) 857.20/297.03 , a__plus(N, s(M)) -> s(a__plus(mark(N), mark(M))) } 857.20/297.03 Weak Trs: 857.20/297.03 { a__and(X1, X2) -> and(X1, X2) 857.20/297.03 , a__and(tt(), X) -> mark(X) 857.20/297.03 , mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) } 857.20/297.03 Obligation: 857.20/297.03 innermost runtime complexity 857.20/297.03 Answer: 857.20/297.03 MAYBE 857.20/297.03 857.20/297.03 The weightgap principle applies (using the following nonconstant 857.20/297.03 growth matrix-interpretation) 857.20/297.03 857.20/297.03 The following argument positions are usable: 857.20/297.03 Uargs(a__and) = {1}, Uargs(a__plus) = {1, 2}, Uargs(s) = {1} 857.20/297.03 857.20/297.03 TcT has computed the following matrix interpretation satisfying 857.20/297.03 not(EDA) and not(IDA(1)). 857.20/297.03 857.20/297.03 [a__and](x1, x2) = [1] x1 + [0] 857.20/297.03 857.20/297.03 [tt] = [0] 857.20/297.03 857.20/297.03 [mark](x1) = [0] 857.20/297.03 857.20/297.03 [a__plus](x1, x2) = [1] x1 + [1] x2 + [0] 857.20/297.03 857.20/297.03 [0] = [1] 857.20/297.03 857.20/297.03 [s](x1) = [1] x1 + [0] 857.20/297.03 857.20/297.03 [and](x1, x2) = [1] x1 + [0] 857.20/297.03 857.20/297.03 [plus](x1, x2) = [1] x1 + [1] x2 + [7] 857.20/297.03 857.20/297.03 The order satisfies the following ordering constraints: 857.20/297.03 857.20/297.03 [a__and(X1, X2)] = [1] X1 + [0] 857.20/297.03 >= [1] X1 + [0] 857.20/297.03 = [and(X1, X2)] 857.20/297.03 857.20/297.03 [a__and(tt(), X)] = [0] 857.20/297.03 >= [0] 857.20/297.03 = [mark(X)] 857.20/297.03 857.20/297.03 [mark(tt())] = [0] 857.20/297.03 >= [0] 857.20/297.03 = [tt()] 857.20/297.03 857.20/297.03 [mark(0())] = [0] 857.20/297.03 ? [1] 857.20/297.03 = [0()] 857.20/297.03 857.20/297.03 [mark(s(X))] = [0] 857.20/297.03 >= [0] 857.20/297.03 = [s(mark(X))] 857.20/297.03 857.20/297.03 [mark(and(X1, X2))] = [0] 857.20/297.03 >= [0] 857.20/297.03 = [a__and(mark(X1), X2)] 857.20/297.03 857.20/297.03 [mark(plus(X1, X2))] = [0] 857.20/297.03 >= [0] 857.20/297.03 = [a__plus(mark(X1), mark(X2))] 857.20/297.03 857.20/297.03 [a__plus(X1, X2)] = [1] X1 + [1] X2 + [0] 857.20/297.03 ? [1] X1 + [1] X2 + [7] 857.20/297.03 = [plus(X1, X2)] 857.20/297.03 857.20/297.03 [a__plus(N, 0())] = [1] N + [1] 857.20/297.03 > [0] 857.20/297.03 = [mark(N)] 857.20/297.03 857.20/297.03 [a__plus(N, s(M))] = [1] N + [1] M + [0] 857.20/297.03 >= [0] 857.20/297.03 = [s(a__plus(mark(N), mark(M)))] 857.20/297.03 857.20/297.03 857.20/297.03 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 857.20/297.03 857.20/297.03 We are left with following problem, upon which TcT provides the 857.20/297.03 certificate MAYBE. 857.20/297.03 857.20/297.03 Strict Trs: 857.20/297.03 { mark(tt()) -> tt() 857.20/297.03 , mark(0()) -> 0() 857.20/297.03 , mark(s(X)) -> s(mark(X)) 857.20/297.03 , mark(and(X1, X2)) -> a__and(mark(X1), X2) 857.20/297.03 , a__plus(X1, X2) -> plus(X1, X2) 857.20/297.03 , a__plus(N, s(M)) -> s(a__plus(mark(N), mark(M))) } 857.20/297.03 Weak Trs: 857.20/297.03 { a__and(X1, X2) -> and(X1, X2) 857.20/297.03 , a__and(tt(), X) -> mark(X) 857.20/297.03 , mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) 857.20/297.03 , a__plus(N, 0()) -> mark(N) } 857.20/297.03 Obligation: 857.20/297.03 innermost runtime complexity 857.20/297.03 Answer: 857.20/297.03 MAYBE 857.20/297.03 857.20/297.03 The weightgap principle applies (using the following nonconstant 857.20/297.03 growth matrix-interpretation) 857.20/297.03 857.20/297.03 The following argument positions are usable: 857.20/297.03 Uargs(a__and) = {1}, Uargs(a__plus) = {1, 2}, Uargs(s) = {1} 857.20/297.03 857.20/297.03 TcT has computed the following matrix interpretation satisfying 857.20/297.03 not(EDA) and not(IDA(1)). 857.20/297.03 857.20/297.03 [a__and](x1, x2) = [1] x1 + [1] x2 + [7] 857.20/297.03 857.20/297.03 [tt] = [4] 857.20/297.03 857.20/297.03 [mark](x1) = [1] x1 + [1] 857.20/297.03 857.20/297.03 [a__plus](x1, x2) = [1] x1 + [1] x2 + [0] 857.20/297.03 857.20/297.03 [0] = [4] 857.20/297.03 857.20/297.03 [s](x1) = [1] x1 + [0] 857.20/297.03 857.20/297.03 [and](x1, x2) = [1] x1 + [1] x2 + [0] 857.20/297.03 857.20/297.03 [plus](x1, x2) = [1] x1 + [1] x2 + [2] 857.20/297.03 857.20/297.03 The order satisfies the following ordering constraints: 857.20/297.03 857.20/297.03 [a__and(X1, X2)] = [1] X1 + [1] X2 + [7] 857.20/297.03 > [1] X1 + [1] X2 + [0] 857.20/297.03 = [and(X1, X2)] 857.20/297.03 857.20/297.03 [a__and(tt(), X)] = [1] X + [11] 857.20/297.03 > [1] X + [1] 857.20/297.03 = [mark(X)] 857.20/297.03 857.20/297.03 [mark(tt())] = [5] 857.20/297.03 > [4] 857.20/297.03 = [tt()] 857.20/297.03 857.20/297.03 [mark(0())] = [5] 857.20/297.03 > [4] 857.20/297.03 = [0()] 857.20/297.03 857.20/297.03 [mark(s(X))] = [1] X + [1] 857.20/297.03 >= [1] X + [1] 857.20/297.03 = [s(mark(X))] 857.20/297.03 857.20/297.03 [mark(and(X1, X2))] = [1] X1 + [1] X2 + [1] 857.20/297.03 ? [1] X1 + [1] X2 + [8] 857.20/297.03 = [a__and(mark(X1), X2)] 857.20/297.03 857.20/297.03 [mark(plus(X1, X2))] = [1] X1 + [1] X2 + [3] 857.20/297.03 > [1] X1 + [1] X2 + [2] 857.20/297.03 = [a__plus(mark(X1), mark(X2))] 857.20/297.03 857.20/297.03 [a__plus(X1, X2)] = [1] X1 + [1] X2 + [0] 857.20/297.03 ? [1] X1 + [1] X2 + [2] 857.20/297.03 = [plus(X1, X2)] 857.20/297.03 857.20/297.03 [a__plus(N, 0())] = [1] N + [4] 857.20/297.03 > [1] N + [1] 857.20/297.03 = [mark(N)] 857.20/297.03 857.20/297.03 [a__plus(N, s(M))] = [1] N + [1] M + [0] 857.20/297.03 ? [1] N + [1] M + [2] 857.20/297.03 = [s(a__plus(mark(N), mark(M)))] 857.20/297.03 857.20/297.03 857.20/297.03 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 857.20/297.03 857.20/297.03 We are left with following problem, upon which TcT provides the 857.20/297.03 certificate MAYBE. 857.20/297.03 857.20/297.03 Strict Trs: 857.20/297.03 { mark(s(X)) -> s(mark(X)) 857.20/297.03 , mark(and(X1, X2)) -> a__and(mark(X1), X2) 857.20/297.03 , a__plus(X1, X2) -> plus(X1, X2) 857.20/297.03 , a__plus(N, s(M)) -> s(a__plus(mark(N), mark(M))) } 857.20/297.03 Weak Trs: 857.20/297.03 { a__and(X1, X2) -> and(X1, X2) 857.20/297.03 , a__and(tt(), X) -> mark(X) 857.20/297.03 , mark(tt()) -> tt() 857.20/297.03 , mark(0()) -> 0() 857.20/297.03 , mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) 857.20/297.03 , a__plus(N, 0()) -> mark(N) } 857.20/297.03 Obligation: 857.20/297.03 innermost runtime complexity 857.20/297.03 Answer: 857.20/297.03 MAYBE 857.20/297.03 857.20/297.03 None of the processors succeeded. 857.20/297.03 857.20/297.03 Details of failed attempt(s): 857.20/297.03 ----------------------------- 857.20/297.03 1) 'empty' failed due to the following reason: 857.20/297.03 857.20/297.03 Empty strict component of the problem is NOT empty. 857.20/297.03 857.20/297.03 2) 'With Problem ...' failed due to the following reason: 857.20/297.03 857.20/297.03 None of the processors succeeded. 857.20/297.03 857.20/297.03 Details of failed attempt(s): 857.20/297.03 ----------------------------- 857.20/297.03 1) 'empty' failed due to the following reason: 857.20/297.03 857.20/297.03 Empty strict component of the problem is NOT empty. 857.20/297.03 857.20/297.03 2) 'Fastest' failed due to the following reason: 857.20/297.03 857.20/297.03 None of the processors succeeded. 857.20/297.03 857.20/297.03 Details of failed attempt(s): 857.20/297.03 ----------------------------- 857.20/297.03 1) 'With Problem ...' failed due to the following reason: 857.20/297.03 857.20/297.03 None of the processors succeeded. 857.20/297.03 857.20/297.03 Details of failed attempt(s): 857.20/297.03 ----------------------------- 857.20/297.03 1) 'empty' failed due to the following reason: 857.20/297.03 857.20/297.03 Empty strict component of the problem is NOT empty. 857.20/297.03 857.20/297.03 2) 'With Problem ...' failed due to the following reason: 857.20/297.03 857.20/297.03 We use the processor 'matrix interpretation of dimension 2' to 857.20/297.03 orient following rules strictly. 857.20/297.03 857.20/297.03 Trs: { a__plus(N, s(M)) -> s(a__plus(mark(N), mark(M))) } 857.20/297.03 857.20/297.03 The induced complexity on above rules (modulo remaining rules) is 857.20/297.03 YES(?,O(n^2)) . These rules are moved into the corresponding weak 857.20/297.03 component(s). 857.20/297.03 857.20/297.03 Sub-proof: 857.20/297.03 ---------- 857.20/297.03 The following argument positions are usable: 857.20/297.03 Uargs(a__and) = {1}, Uargs(a__plus) = {1, 2}, Uargs(s) = {1} 857.20/297.03 857.20/297.03 TcT has computed the following constructor-based matrix 857.20/297.03 interpretation satisfying not(EDA). 857.20/297.03 857.20/297.03 [a__and](x1, x2) = [1 0] x1 + [1 0] x2 + [0] 857.20/297.03 [0 0] [0 1] [0] 857.20/297.03 857.20/297.03 [tt] = [0] 857.20/297.03 [0] 857.20/297.03 857.20/297.03 [mark](x1) = [1 0] x1 + [0] 857.20/297.03 [0 1] [0] 857.20/297.03 857.20/297.03 [a__plus](x1, x2) = [1 0] x1 + [1 1] x2 + [0] 857.20/297.03 [0 1] [0 1] [0] 857.20/297.03 857.20/297.03 [0] = [0] 857.20/297.03 [0] 857.20/297.03 857.20/297.03 [s](x1) = [1 0] x1 + [0] 857.20/297.03 [0 1] [1] 857.20/297.03 857.20/297.03 [and](x1, x2) = [1 0] x1 + [1 0] x2 + [0] 857.20/297.03 [0 0] [0 1] [0] 857.20/297.03 857.20/297.03 [plus](x1, x2) = [1 0] x1 + [1 1] x2 + [0] 857.20/297.03 [0 1] [0 1] [0] 857.20/297.03 857.20/297.03 The order satisfies the following ordering constraints: 857.20/297.04 857.20/297.04 [a__and(X1, X2)] = [1 0] X1 + [1 0] X2 + [0] 857.20/297.04 [0 0] [0 1] [0] 857.20/297.04 >= [1 0] X1 + [1 0] X2 + [0] 857.20/297.04 [0 0] [0 1] [0] 857.20/297.04 = [and(X1, X2)] 857.20/297.04 857.20/297.04 [a__and(tt(), X)] = [1 0] X + [0] 857.20/297.04 [0 1] [0] 857.20/297.04 >= [1 0] X + [0] 857.20/297.04 [0 1] [0] 857.20/297.04 = [mark(X)] 857.20/297.04 857.20/297.04 [mark(tt())] = [0] 857.20/297.04 [0] 857.20/297.04 >= [0] 857.20/297.04 [0] 857.20/297.04 = [tt()] 857.20/297.04 857.20/297.04 [mark(0())] = [0] 857.20/297.04 [0] 857.20/297.04 >= [0] 857.20/297.04 [0] 857.20/297.04 = [0()] 857.20/297.04 857.20/297.04 [mark(s(X))] = [1 0] X + [0] 857.20/297.04 [0 1] [1] 857.20/297.04 >= [1 0] X + [0] 857.20/297.04 [0 1] [1] 857.20/297.04 = [s(mark(X))] 857.20/297.04 857.20/297.04 [mark(and(X1, X2))] = [1 0] X1 + [1 0] X2 + [0] 857.20/297.04 [0 0] [0 1] [0] 857.20/297.04 >= [1 0] X1 + [1 0] X2 + [0] 857.20/297.04 [0 0] [0 1] [0] 857.20/297.04 = [a__and(mark(X1), X2)] 857.20/297.04 857.20/297.04 [mark(plus(X1, X2))] = [1 0] X1 + [1 1] X2 + [0] 857.20/297.04 [0 1] [0 1] [0] 857.20/297.04 >= [1 0] X1 + [1 1] X2 + [0] 857.20/297.04 [0 1] [0 1] [0] 857.20/297.04 = [a__plus(mark(X1), mark(X2))] 857.20/297.04 857.20/297.04 [a__plus(X1, X2)] = [1 0] X1 + [1 1] X2 + [0] 857.20/297.04 [0 1] [0 1] [0] 857.20/297.04 >= [1 0] X1 + [1 1] X2 + [0] 857.20/297.04 [0 1] [0 1] [0] 857.20/297.04 = [plus(X1, X2)] 857.20/297.04 857.20/297.04 [a__plus(N, 0())] = [1 0] N + [0] 857.20/297.04 [0 1] [0] 857.20/297.04 >= [1 0] N + [0] 857.20/297.04 [0 1] [0] 857.20/297.04 = [mark(N)] 857.20/297.04 857.20/297.04 [a__plus(N, s(M))] = [1 0] N + [1 1] M + [1] 857.20/297.04 [0 1] [0 1] [1] 857.20/297.04 > [1 0] N + [1 1] M + [0] 857.20/297.04 [0 1] [0 1] [1] 857.20/297.04 = [s(a__plus(mark(N), mark(M)))] 857.20/297.04 857.20/297.04 857.20/297.04 We return to the main proof. 857.20/297.04 857.20/297.04 We are left with following problem, upon which TcT provides the 857.20/297.04 certificate MAYBE. 857.20/297.04 857.20/297.04 Strict Trs: 857.20/297.04 { mark(s(X)) -> s(mark(X)) 857.20/297.04 , mark(and(X1, X2)) -> a__and(mark(X1), X2) 857.20/297.04 , a__plus(X1, X2) -> plus(X1, X2) } 857.20/297.04 Weak Trs: 857.20/297.04 { a__and(X1, X2) -> and(X1, X2) 857.20/297.04 , a__and(tt(), X) -> mark(X) 857.20/297.04 , mark(tt()) -> tt() 857.20/297.04 , mark(0()) -> 0() 857.20/297.04 , mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) 857.20/297.04 , a__plus(N, 0()) -> mark(N) 857.20/297.04 , a__plus(N, s(M)) -> s(a__plus(mark(N), mark(M))) } 857.20/297.04 Obligation: 857.20/297.04 innermost runtime complexity 857.20/297.04 Answer: 857.20/297.04 MAYBE 857.20/297.04 857.20/297.04 None of the processors succeeded. 857.20/297.04 857.20/297.04 Details of failed attempt(s): 857.20/297.04 ----------------------------- 857.20/297.04 1) 'empty' failed due to the following reason: 857.20/297.04 857.20/297.04 Empty strict component of the problem is NOT empty. 857.20/297.04 857.20/297.04 2) 'With Problem ...' failed due to the following reason: 857.20/297.04 857.20/297.04 None of the processors succeeded. 857.20/297.04 857.20/297.04 Details of failed attempt(s): 857.20/297.04 ----------------------------- 857.20/297.04 1) 'empty' failed due to the following reason: 857.20/297.04 857.20/297.04 Empty strict component of the problem is NOT empty. 857.20/297.04 857.20/297.04 2) 'With Problem ...' failed due to the following reason: 857.20/297.04 857.20/297.04 Empty strict component of the problem is NOT empty. 857.20/297.04 857.20/297.04 857.20/297.04 857.20/297.04 857.20/297.04 2) 'With Problem ...' failed due to the following reason: 857.20/297.04 857.20/297.04 None of the processors succeeded. 857.20/297.04 857.20/297.04 Details of failed attempt(s): 857.20/297.04 ----------------------------- 857.20/297.04 1) 'empty' failed due to the following reason: 857.20/297.04 857.20/297.04 Empty strict component of the problem is NOT empty. 857.20/297.04 857.20/297.04 2) 'With Problem ...' failed due to the following reason: 857.20/297.04 857.20/297.04 Empty strict component of the problem is NOT empty. 857.20/297.04 857.20/297.04 857.20/297.04 857.20/297.04 857.20/297.04 857.20/297.04 2) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 857.20/297.04 failed due to the following reason: 857.20/297.04 857.20/297.04 Computation stopped due to timeout after 24.0 seconds. 857.20/297.04 857.20/297.04 3) 'Best' failed due to the following reason: 857.20/297.04 857.20/297.04 None of the processors succeeded. 857.20/297.04 857.20/297.04 Details of failed attempt(s): 857.20/297.04 ----------------------------- 857.20/297.04 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 857.20/297.04 following reason: 857.20/297.04 857.20/297.04 The input cannot be shown compatible 857.20/297.04 857.20/297.04 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 857.20/297.04 to the following reason: 857.20/297.04 857.20/297.04 The input cannot be shown compatible 857.20/297.04 857.20/297.04 857.20/297.04 857.20/297.04 857.20/297.04 857.20/297.04 Arrrr.. 857.43/297.23 EOF