MAYBE 882.30/297.07 MAYBE 882.30/297.07 882.30/297.07 We are left with following problem, upon which TcT provides the 882.30/297.07 certificate MAYBE. 882.30/297.07 882.30/297.07 Strict Trs: 882.30/297.07 { fib(0()) -> 0() 882.30/297.07 , fib(s(0())) -> s(0()) 882.30/297.07 , fib(s(s(x))) -> sp(g(x)) 882.30/297.07 , fib(s(s(0()))) -> s(0()) 882.30/297.07 , sp(pair(x, y)) -> +(x, y) 882.30/297.07 , g(0()) -> pair(s(0()), 0()) 882.30/297.07 , g(s(x)) -> np(g(x)) 882.30/297.07 , g(s(0())) -> pair(s(0()), s(0())) 882.30/297.07 , np(pair(x, y)) -> pair(+(x, y), x) 882.30/297.07 , +(x, 0()) -> x 882.30/297.07 , +(x, s(y)) -> s(+(x, y)) } 882.30/297.07 Obligation: 882.30/297.07 innermost runtime complexity 882.30/297.07 Answer: 882.30/297.07 MAYBE 882.30/297.07 882.30/297.07 None of the processors succeeded. 882.30/297.07 882.30/297.07 Details of failed attempt(s): 882.30/297.07 ----------------------------- 882.30/297.07 1) 'empty' failed due to the following reason: 882.30/297.07 882.30/297.07 Empty strict component of the problem is NOT empty. 882.30/297.07 882.30/297.07 2) 'Best' failed due to the following reason: 882.30/297.07 882.30/297.07 None of the processors succeeded. 882.30/297.07 882.30/297.07 Details of failed attempt(s): 882.30/297.07 ----------------------------- 882.30/297.07 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 882.30/297.07 following reason: 882.30/297.07 882.30/297.07 Computation stopped due to timeout after 297.0 seconds. 882.30/297.07 882.30/297.07 2) 'Best' failed due to the following reason: 882.30/297.07 882.30/297.07 None of the processors succeeded. 882.30/297.07 882.30/297.07 Details of failed attempt(s): 882.30/297.07 ----------------------------- 882.30/297.07 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 882.30/297.07 seconds)' failed due to the following reason: 882.30/297.07 882.30/297.07 The weightgap principle applies (using the following nonconstant 882.30/297.07 growth matrix-interpretation) 882.30/297.07 882.30/297.07 The following argument positions are usable: 882.30/297.07 Uargs(s) = {1}, Uargs(sp) = {1}, Uargs(pair) = {1}, Uargs(np) = {1} 882.30/297.07 882.30/297.07 TcT has computed the following matrix interpretation satisfying 882.30/297.07 not(EDA) and not(IDA(1)). 882.30/297.07 882.30/297.07 [fib](x1) = [0] 882.30/297.07 882.30/297.07 [0] = [0] 882.30/297.07 882.30/297.07 [s](x1) = [1] x1 + [0] 882.30/297.07 882.30/297.07 [sp](x1) = [1] x1 + [0] 882.30/297.07 882.30/297.07 [g](x1) = [0] 882.30/297.07 882.30/297.07 [pair](x1, x2) = [1] x1 + [0] 882.30/297.07 882.30/297.07 [np](x1) = [1] x1 + [0] 882.30/297.07 882.30/297.07 [+](x1, x2) = [1] x1 + [1] 882.30/297.07 882.30/297.07 The order satisfies the following ordering constraints: 882.30/297.07 882.30/297.07 [fib(0())] = [0] 882.30/297.07 >= [0] 882.30/297.07 = [0()] 882.30/297.07 882.30/297.07 [fib(s(0()))] = [0] 882.30/297.07 >= [0] 882.30/297.07 = [s(0())] 882.30/297.07 882.30/297.07 [fib(s(s(x)))] = [0] 882.30/297.07 >= [0] 882.30/297.07 = [sp(g(x))] 882.30/297.07 882.30/297.07 [fib(s(s(0())))] = [0] 882.30/297.07 >= [0] 882.30/297.07 = [s(0())] 882.30/297.07 882.30/297.07 [sp(pair(x, y))] = [1] x + [0] 882.30/297.07 ? [1] x + [1] 882.30/297.07 = [+(x, y)] 882.30/297.07 882.30/297.07 [g(0())] = [0] 882.30/297.07 >= [0] 882.30/297.07 = [pair(s(0()), 0())] 882.30/297.07 882.30/297.07 [g(s(x))] = [0] 882.30/297.07 >= [0] 882.30/297.07 = [np(g(x))] 882.30/297.07 882.30/297.07 [g(s(0()))] = [0] 882.30/297.07 >= [0] 882.30/297.07 = [pair(s(0()), s(0()))] 882.30/297.07 882.30/297.07 [np(pair(x, y))] = [1] x + [0] 882.30/297.07 ? [1] x + [1] 882.30/297.07 = [pair(+(x, y), x)] 882.30/297.07 882.30/297.07 [+(x, 0())] = [1] x + [1] 882.30/297.07 > [1] x + [0] 882.30/297.07 = [x] 882.30/297.07 882.30/297.07 [+(x, s(y))] = [1] x + [1] 882.30/297.07 >= [1] x + [1] 882.30/297.07 = [s(+(x, y))] 882.30/297.07 882.30/297.07 882.30/297.07 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 882.30/297.07 882.30/297.07 We are left with following problem, upon which TcT provides the 882.30/297.07 certificate MAYBE. 882.30/297.07 882.30/297.07 Strict Trs: 882.30/297.07 { fib(0()) -> 0() 882.30/297.07 , fib(s(0())) -> s(0()) 882.30/297.07 , fib(s(s(x))) -> sp(g(x)) 882.30/297.07 , fib(s(s(0()))) -> s(0()) 882.30/297.07 , sp(pair(x, y)) -> +(x, y) 882.30/297.07 , g(0()) -> pair(s(0()), 0()) 882.30/297.07 , g(s(x)) -> np(g(x)) 882.30/297.07 , g(s(0())) -> pair(s(0()), s(0())) 882.30/297.07 , np(pair(x, y)) -> pair(+(x, y), x) 882.30/297.07 , +(x, s(y)) -> s(+(x, y)) } 882.30/297.07 Weak Trs: { +(x, 0()) -> x } 882.30/297.07 Obligation: 882.30/297.07 innermost runtime complexity 882.30/297.07 Answer: 882.30/297.07 MAYBE 882.30/297.07 882.30/297.07 The weightgap principle applies (using the following nonconstant 882.30/297.07 growth matrix-interpretation) 882.30/297.07 882.30/297.07 The following argument positions are usable: 882.30/297.07 Uargs(s) = {1}, Uargs(sp) = {1}, Uargs(pair) = {1}, Uargs(np) = {1} 882.30/297.07 882.30/297.07 TcT has computed the following matrix interpretation satisfying 882.30/297.07 not(EDA) and not(IDA(1)). 882.30/297.07 882.30/297.07 [fib](x1) = [0] 882.30/297.07 882.30/297.07 [0] = [0] 882.30/297.07 882.30/297.07 [s](x1) = [1] x1 + [0] 882.30/297.07 882.30/297.07 [sp](x1) = [1] x1 + [6] 882.30/297.07 882.30/297.07 [g](x1) = [2] 882.30/297.07 882.30/297.07 [pair](x1, x2) = [1] x1 + [4] 882.30/297.07 882.30/297.07 [np](x1) = [1] x1 + [0] 882.30/297.07 882.30/297.07 [+](x1, x2) = [1] x1 + [0] 882.30/297.07 882.30/297.07 The order satisfies the following ordering constraints: 882.30/297.07 882.30/297.07 [fib(0())] = [0] 882.30/297.07 >= [0] 882.30/297.07 = [0()] 882.30/297.07 882.30/297.07 [fib(s(0()))] = [0] 882.30/297.07 >= [0] 882.30/297.07 = [s(0())] 882.30/297.07 882.30/297.07 [fib(s(s(x)))] = [0] 882.30/297.07 ? [8] 882.30/297.07 = [sp(g(x))] 882.30/297.07 882.30/297.07 [fib(s(s(0())))] = [0] 882.30/297.07 >= [0] 882.30/297.07 = [s(0())] 882.30/297.07 882.30/297.07 [sp(pair(x, y))] = [1] x + [10] 882.30/297.07 > [1] x + [0] 882.30/297.07 = [+(x, y)] 882.30/297.07 882.30/297.07 [g(0())] = [2] 882.30/297.07 ? [4] 882.30/297.07 = [pair(s(0()), 0())] 882.30/297.07 882.30/297.07 [g(s(x))] = [2] 882.30/297.07 >= [2] 882.30/297.07 = [np(g(x))] 882.30/297.07 882.30/297.07 [g(s(0()))] = [2] 882.30/297.07 ? [4] 882.30/297.07 = [pair(s(0()), s(0()))] 882.30/297.07 882.30/297.07 [np(pair(x, y))] = [1] x + [4] 882.30/297.07 >= [1] x + [4] 882.30/297.07 = [pair(+(x, y), x)] 882.30/297.07 882.30/297.07 [+(x, 0())] = [1] x + [0] 882.30/297.07 >= [1] x + [0] 882.30/297.07 = [x] 882.30/297.07 882.30/297.07 [+(x, s(y))] = [1] x + [0] 882.30/297.07 >= [1] x + [0] 882.30/297.07 = [s(+(x, y))] 882.30/297.07 882.30/297.07 882.30/297.07 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 882.30/297.07 882.30/297.07 We are left with following problem, upon which TcT provides the 882.30/297.07 certificate MAYBE. 882.30/297.07 882.30/297.07 Strict Trs: 882.30/297.07 { fib(0()) -> 0() 882.30/297.07 , fib(s(0())) -> s(0()) 882.30/297.07 , fib(s(s(x))) -> sp(g(x)) 882.30/297.07 , fib(s(s(0()))) -> s(0()) 882.30/297.07 , g(0()) -> pair(s(0()), 0()) 882.30/297.07 , g(s(x)) -> np(g(x)) 882.30/297.07 , g(s(0())) -> pair(s(0()), s(0())) 882.30/297.07 , np(pair(x, y)) -> pair(+(x, y), x) 882.30/297.07 , +(x, s(y)) -> s(+(x, y)) } 882.30/297.07 Weak Trs: 882.30/297.07 { sp(pair(x, y)) -> +(x, y) 882.30/297.07 , +(x, 0()) -> x } 882.30/297.07 Obligation: 882.30/297.07 innermost runtime complexity 882.30/297.07 Answer: 882.30/297.07 MAYBE 882.30/297.07 882.30/297.07 The weightgap principle applies (using the following nonconstant 882.30/297.07 growth matrix-interpretation) 882.30/297.07 882.30/297.07 The following argument positions are usable: 882.30/297.07 Uargs(s) = {1}, Uargs(sp) = {1}, Uargs(pair) = {1}, Uargs(np) = {1} 882.30/297.07 882.30/297.07 TcT has computed the following matrix interpretation satisfying 882.30/297.07 not(EDA) and not(IDA(1)). 882.30/297.07 882.30/297.07 [fib](x1) = [0] 882.30/297.07 882.30/297.07 [0] = [0] 882.30/297.07 882.30/297.07 [s](x1) = [1] x1 + [0] 882.30/297.07 882.30/297.07 [sp](x1) = [1] x1 + [0] 882.30/297.07 882.30/297.07 [g](x1) = [0] 882.30/297.07 882.30/297.07 [pair](x1, x2) = [1] x1 + [0] 882.30/297.07 882.30/297.07 [np](x1) = [1] x1 + [4] 882.30/297.07 882.30/297.07 [+](x1, x2) = [1] x1 + [0] 882.30/297.07 882.30/297.07 The order satisfies the following ordering constraints: 882.30/297.07 882.30/297.07 [fib(0())] = [0] 882.30/297.07 >= [0] 882.30/297.07 = [0()] 882.30/297.07 882.30/297.07 [fib(s(0()))] = [0] 882.30/297.07 >= [0] 882.30/297.07 = [s(0())] 882.30/297.07 882.30/297.07 [fib(s(s(x)))] = [0] 882.30/297.07 >= [0] 882.30/297.07 = [sp(g(x))] 882.30/297.07 882.30/297.07 [fib(s(s(0())))] = [0] 882.30/297.07 >= [0] 882.30/297.07 = [s(0())] 882.30/297.07 882.30/297.07 [sp(pair(x, y))] = [1] x + [0] 882.30/297.07 >= [1] x + [0] 882.30/297.07 = [+(x, y)] 882.30/297.07 882.30/297.07 [g(0())] = [0] 882.30/297.07 >= [0] 882.30/297.07 = [pair(s(0()), 0())] 882.30/297.07 882.30/297.07 [g(s(x))] = [0] 882.30/297.07 ? [4] 882.30/297.07 = [np(g(x))] 882.30/297.07 882.30/297.07 [g(s(0()))] = [0] 882.30/297.07 >= [0] 882.30/297.07 = [pair(s(0()), s(0()))] 882.30/297.07 882.30/297.07 [np(pair(x, y))] = [1] x + [4] 882.30/297.07 > [1] x + [0] 882.30/297.07 = [pair(+(x, y), x)] 882.30/297.07 882.30/297.07 [+(x, 0())] = [1] x + [0] 882.30/297.07 >= [1] x + [0] 882.30/297.07 = [x] 882.30/297.07 882.30/297.07 [+(x, s(y))] = [1] x + [0] 882.30/297.07 >= [1] x + [0] 882.30/297.07 = [s(+(x, y))] 882.30/297.07 882.30/297.07 882.30/297.07 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 882.30/297.07 882.30/297.07 We are left with following problem, upon which TcT provides the 882.30/297.07 certificate MAYBE. 882.30/297.07 882.30/297.07 Strict Trs: 882.30/297.07 { fib(0()) -> 0() 882.30/297.07 , fib(s(0())) -> s(0()) 882.30/297.07 , fib(s(s(x))) -> sp(g(x)) 882.30/297.07 , fib(s(s(0()))) -> s(0()) 882.30/297.07 , g(0()) -> pair(s(0()), 0()) 882.30/297.07 , g(s(x)) -> np(g(x)) 882.30/297.07 , g(s(0())) -> pair(s(0()), s(0())) 882.30/297.07 , +(x, s(y)) -> s(+(x, y)) } 882.30/297.07 Weak Trs: 882.30/297.07 { sp(pair(x, y)) -> +(x, y) 882.30/297.07 , np(pair(x, y)) -> pair(+(x, y), x) 882.30/297.07 , +(x, 0()) -> x } 882.30/297.07 Obligation: 882.30/297.07 innermost runtime complexity 882.30/297.07 Answer: 882.30/297.07 MAYBE 882.30/297.07 882.30/297.07 The weightgap principle applies (using the following nonconstant 882.30/297.07 growth matrix-interpretation) 882.30/297.07 882.30/297.07 The following argument positions are usable: 882.30/297.07 Uargs(s) = {1}, Uargs(sp) = {1}, Uargs(pair) = {1}, Uargs(np) = {1} 882.30/297.07 882.30/297.07 TcT has computed the following matrix interpretation satisfying 882.30/297.07 not(EDA) and not(IDA(1)). 882.30/297.07 882.30/297.07 [fib](x1) = [0] 882.30/297.07 882.30/297.07 [0] = [0] 882.30/297.07 882.30/297.07 [s](x1) = [1] x1 + [0] 882.30/297.07 882.30/297.07 [sp](x1) = [1] x1 + [4] 882.30/297.07 882.30/297.07 [g](x1) = [4] 882.30/297.07 882.30/297.07 [pair](x1, x2) = [1] x1 + [0] 882.30/297.07 882.30/297.07 [np](x1) = [1] x1 + [0] 882.30/297.07 882.30/297.07 [+](x1, x2) = [1] x1 + [0] 882.30/297.07 882.30/297.07 The order satisfies the following ordering constraints: 882.30/297.07 882.30/297.07 [fib(0())] = [0] 882.30/297.07 >= [0] 882.30/297.07 = [0()] 882.30/297.07 882.30/297.07 [fib(s(0()))] = [0] 882.30/297.07 >= [0] 882.30/297.07 = [s(0())] 882.30/297.07 882.30/297.07 [fib(s(s(x)))] = [0] 882.30/297.07 ? [8] 882.30/297.07 = [sp(g(x))] 882.30/297.07 882.30/297.07 [fib(s(s(0())))] = [0] 882.30/297.07 >= [0] 882.30/297.07 = [s(0())] 882.30/297.07 882.30/297.07 [sp(pair(x, y))] = [1] x + [4] 882.30/297.07 > [1] x + [0] 882.30/297.07 = [+(x, y)] 882.30/297.07 882.30/297.07 [g(0())] = [4] 882.30/297.07 > [0] 882.30/297.07 = [pair(s(0()), 0())] 882.30/297.07 882.30/297.07 [g(s(x))] = [4] 882.30/297.07 >= [4] 882.30/297.07 = [np(g(x))] 882.30/297.07 882.30/297.07 [g(s(0()))] = [4] 882.30/297.07 > [0] 882.30/297.07 = [pair(s(0()), s(0()))] 882.30/297.07 882.30/297.07 [np(pair(x, y))] = [1] x + [0] 882.30/297.07 >= [1] x + [0] 882.30/297.07 = [pair(+(x, y), x)] 882.30/297.07 882.30/297.07 [+(x, 0())] = [1] x + [0] 882.30/297.07 >= [1] x + [0] 882.30/297.07 = [x] 882.30/297.07 882.30/297.07 [+(x, s(y))] = [1] x + [0] 882.30/297.07 >= [1] x + [0] 882.30/297.07 = [s(+(x, y))] 882.30/297.07 882.30/297.07 882.30/297.07 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 882.30/297.07 882.30/297.07 We are left with following problem, upon which TcT provides the 882.30/297.07 certificate MAYBE. 882.30/297.07 882.30/297.07 Strict Trs: 882.30/297.07 { fib(0()) -> 0() 882.30/297.07 , fib(s(0())) -> s(0()) 882.30/297.07 , fib(s(s(x))) -> sp(g(x)) 882.30/297.07 , fib(s(s(0()))) -> s(0()) 882.30/297.07 , g(s(x)) -> np(g(x)) 882.30/297.07 , +(x, s(y)) -> s(+(x, y)) } 882.30/297.07 Weak Trs: 882.30/297.07 { sp(pair(x, y)) -> +(x, y) 882.30/297.07 , g(0()) -> pair(s(0()), 0()) 882.30/297.07 , g(s(0())) -> pair(s(0()), s(0())) 882.30/297.07 , np(pair(x, y)) -> pair(+(x, y), x) 882.30/297.07 , +(x, 0()) -> x } 882.30/297.07 Obligation: 882.30/297.07 innermost runtime complexity 882.30/297.07 Answer: 882.30/297.07 MAYBE 882.30/297.07 882.30/297.07 The weightgap principle applies (using the following nonconstant 882.30/297.07 growth matrix-interpretation) 882.30/297.07 882.30/297.07 The following argument positions are usable: 882.30/297.07 Uargs(s) = {1}, Uargs(sp) = {1}, Uargs(pair) = {1}, Uargs(np) = {1} 882.30/297.07 882.30/297.07 TcT has computed the following matrix interpretation satisfying 882.30/297.07 not(EDA) and not(IDA(1)). 882.30/297.07 882.30/297.07 [fib](x1) = [1] x1 + [0] 882.30/297.07 882.30/297.07 [0] = [4] 882.30/297.07 882.30/297.07 [s](x1) = [1] x1 + [4] 882.30/297.07 882.30/297.07 [sp](x1) = [1] x1 + [3] 882.30/297.07 882.30/297.07 [g](x1) = [1] x1 + [5] 882.30/297.07 882.30/297.07 [pair](x1, x2) = [1] x1 + [1] 882.30/297.07 882.30/297.07 [np](x1) = [1] x1 + [0] 882.30/297.07 882.30/297.07 [+](x1, x2) = [1] x1 + [0] 882.30/297.07 882.30/297.07 The order satisfies the following ordering constraints: 882.30/297.07 882.30/297.07 [fib(0())] = [4] 882.30/297.07 >= [4] 882.30/297.07 = [0()] 882.30/297.07 882.30/297.07 [fib(s(0()))] = [8] 882.30/297.07 >= [8] 882.30/297.07 = [s(0())] 882.30/297.07 882.30/297.07 [fib(s(s(x)))] = [1] x + [8] 882.30/297.07 >= [1] x + [8] 882.30/297.07 = [sp(g(x))] 882.30/297.07 882.30/297.07 [fib(s(s(0())))] = [12] 882.30/297.07 > [8] 882.30/297.07 = [s(0())] 882.30/297.07 882.30/297.07 [sp(pair(x, y))] = [1] x + [4] 882.30/297.07 > [1] x + [0] 882.30/297.07 = [+(x, y)] 882.30/297.07 882.30/297.07 [g(0())] = [9] 882.30/297.07 >= [9] 882.30/297.07 = [pair(s(0()), 0())] 882.30/297.07 882.30/297.07 [g(s(x))] = [1] x + [9] 882.30/297.07 > [1] x + [5] 882.30/297.07 = [np(g(x))] 882.30/297.07 882.30/297.07 [g(s(0()))] = [13] 882.30/297.07 > [9] 882.30/297.07 = [pair(s(0()), s(0()))] 882.30/297.07 882.30/297.07 [np(pair(x, y))] = [1] x + [1] 882.30/297.07 >= [1] x + [1] 882.30/297.07 = [pair(+(x, y), x)] 882.30/297.07 882.30/297.07 [+(x, 0())] = [1] x + [0] 882.30/297.07 >= [1] x + [0] 882.30/297.07 = [x] 882.30/297.07 882.30/297.07 [+(x, s(y))] = [1] x + [0] 882.30/297.07 ? [1] x + [4] 882.30/297.07 = [s(+(x, y))] 882.30/297.07 882.30/297.07 882.30/297.07 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 882.30/297.07 882.30/297.07 We are left with following problem, upon which TcT provides the 882.30/297.07 certificate MAYBE. 882.30/297.07 882.30/297.07 Strict Trs: 882.30/297.07 { fib(0()) -> 0() 882.30/297.07 , fib(s(0())) -> s(0()) 882.30/297.07 , fib(s(s(x))) -> sp(g(x)) 882.30/297.07 , +(x, s(y)) -> s(+(x, y)) } 882.30/297.07 Weak Trs: 882.30/297.07 { fib(s(s(0()))) -> s(0()) 882.30/297.07 , sp(pair(x, y)) -> +(x, y) 882.30/297.07 , g(0()) -> pair(s(0()), 0()) 882.30/297.07 , g(s(x)) -> np(g(x)) 882.30/297.07 , g(s(0())) -> pair(s(0()), s(0())) 882.30/297.07 , np(pair(x, y)) -> pair(+(x, y), x) 882.30/297.07 , +(x, 0()) -> x } 882.30/297.07 Obligation: 882.30/297.07 innermost runtime complexity 882.30/297.07 Answer: 882.30/297.07 MAYBE 882.30/297.07 882.30/297.07 The weightgap principle applies (using the following nonconstant 882.30/297.07 growth matrix-interpretation) 882.30/297.07 882.30/297.07 The following argument positions are usable: 882.30/297.07 Uargs(s) = {1}, Uargs(sp) = {1}, Uargs(pair) = {1}, Uargs(np) = {1} 882.30/297.07 882.30/297.07 TcT has computed the following matrix interpretation satisfying 882.30/297.07 not(EDA) and not(IDA(1)). 882.30/297.07 882.30/297.07 [fib](x1) = [1] x1 + [0] 882.30/297.07 882.30/297.07 [0] = [4] 882.30/297.07 882.30/297.07 [s](x1) = [1] x1 + [4] 882.30/297.07 882.30/297.07 [sp](x1) = [1] x1 + [0] 882.30/297.07 882.30/297.07 [g](x1) = [1] x1 + [4] 882.30/297.07 882.30/297.07 [pair](x1, x2) = [1] x1 + [0] 882.30/297.07 882.30/297.07 [np](x1) = [1] x1 + [4] 882.30/297.07 882.30/297.07 [+](x1, x2) = [1] x1 + [0] 882.30/297.07 882.30/297.07 The order satisfies the following ordering constraints: 882.30/297.07 882.30/297.07 [fib(0())] = [4] 882.30/297.07 >= [4] 882.30/297.07 = [0()] 882.30/297.07 882.30/297.07 [fib(s(0()))] = [8] 882.30/297.07 >= [8] 882.30/297.07 = [s(0())] 882.30/297.07 882.30/297.07 [fib(s(s(x)))] = [1] x + [8] 882.30/297.07 > [1] x + [4] 882.30/297.07 = [sp(g(x))] 882.30/297.07 882.30/297.07 [fib(s(s(0())))] = [12] 882.30/297.07 > [8] 882.30/297.07 = [s(0())] 882.30/297.07 882.30/297.07 [sp(pair(x, y))] = [1] x + [0] 882.30/297.07 >= [1] x + [0] 882.30/297.07 = [+(x, y)] 882.30/297.07 882.30/297.07 [g(0())] = [8] 882.30/297.07 >= [8] 882.30/297.07 = [pair(s(0()), 0())] 882.30/297.07 882.30/297.07 [g(s(x))] = [1] x + [8] 882.30/297.07 >= [1] x + [8] 882.30/297.07 = [np(g(x))] 882.30/297.07 882.30/297.07 [g(s(0()))] = [12] 882.30/297.07 > [8] 882.30/297.07 = [pair(s(0()), s(0()))] 882.30/297.07 882.30/297.07 [np(pair(x, y))] = [1] x + [4] 882.30/297.07 > [1] x + [0] 882.30/297.07 = [pair(+(x, y), x)] 882.30/297.07 882.30/297.07 [+(x, 0())] = [1] x + [0] 882.30/297.07 >= [1] x + [0] 882.30/297.07 = [x] 882.30/297.07 882.30/297.07 [+(x, s(y))] = [1] x + [0] 882.30/297.07 ? [1] x + [4] 882.30/297.07 = [s(+(x, y))] 882.30/297.07 882.30/297.07 882.30/297.07 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 882.30/297.07 882.30/297.07 We are left with following problem, upon which TcT provides the 882.30/297.07 certificate MAYBE. 882.30/297.07 882.30/297.07 Strict Trs: 882.30/297.07 { fib(0()) -> 0() 882.30/297.07 , fib(s(0())) -> s(0()) 882.30/297.07 , +(x, s(y)) -> s(+(x, y)) } 882.30/297.07 Weak Trs: 882.30/297.07 { fib(s(s(x))) -> sp(g(x)) 882.30/297.07 , fib(s(s(0()))) -> s(0()) 882.30/297.07 , sp(pair(x, y)) -> +(x, y) 882.30/297.07 , g(0()) -> pair(s(0()), 0()) 882.30/297.07 , g(s(x)) -> np(g(x)) 882.30/297.07 , g(s(0())) -> pair(s(0()), s(0())) 882.30/297.07 , np(pair(x, y)) -> pair(+(x, y), x) 882.30/297.07 , +(x, 0()) -> x } 882.30/297.07 Obligation: 882.30/297.07 innermost runtime complexity 882.30/297.07 Answer: 882.30/297.07 MAYBE 882.30/297.07 882.30/297.07 The weightgap principle applies (using the following nonconstant 882.30/297.07 growth matrix-interpretation) 882.30/297.07 882.30/297.07 The following argument positions are usable: 882.30/297.07 Uargs(s) = {1}, Uargs(sp) = {1}, Uargs(pair) = {1}, Uargs(np) = {1} 882.30/297.07 882.30/297.07 TcT has computed the following matrix interpretation satisfying 882.30/297.07 not(EDA) and not(IDA(1)). 882.30/297.07 882.30/297.07 [fib](x1) = [1] x1 + [4] 882.30/297.07 882.30/297.07 [0] = [4] 882.30/297.07 882.30/297.07 [s](x1) = [1] x1 + [0] 882.30/297.07 882.30/297.07 [sp](x1) = [1] x1 + [0] 882.30/297.07 882.30/297.07 [g](x1) = [1] x1 + [4] 882.30/297.07 882.30/297.07 [pair](x1, x2) = [1] x1 + [0] 882.30/297.07 882.30/297.07 [np](x1) = [1] x1 + [0] 882.30/297.07 882.30/297.07 [+](x1, x2) = [1] x1 + [0] 882.30/297.07 882.30/297.07 The order satisfies the following ordering constraints: 882.30/297.07 882.30/297.07 [fib(0())] = [8] 882.30/297.07 > [4] 882.30/297.07 = [0()] 882.30/297.07 882.30/297.07 [fib(s(0()))] = [8] 882.30/297.07 > [4] 882.30/297.07 = [s(0())] 882.30/297.07 882.30/297.07 [fib(s(s(x)))] = [1] x + [4] 882.30/297.07 >= [1] x + [4] 882.30/297.07 = [sp(g(x))] 882.30/297.07 882.30/297.07 [fib(s(s(0())))] = [8] 882.30/297.07 > [4] 882.30/297.07 = [s(0())] 882.30/297.07 882.30/297.07 [sp(pair(x, y))] = [1] x + [0] 882.30/297.07 >= [1] x + [0] 882.30/297.07 = [+(x, y)] 882.30/297.07 882.30/297.07 [g(0())] = [8] 882.30/297.07 > [4] 882.30/297.07 = [pair(s(0()), 0())] 882.30/297.07 882.30/297.07 [g(s(x))] = [1] x + [4] 882.30/297.07 >= [1] x + [4] 882.30/297.07 = [np(g(x))] 882.30/297.07 882.30/297.07 [g(s(0()))] = [8] 882.30/297.07 > [4] 882.30/297.07 = [pair(s(0()), s(0()))] 882.30/297.07 882.30/297.07 [np(pair(x, y))] = [1] x + [0] 882.30/297.07 >= [1] x + [0] 882.30/297.07 = [pair(+(x, y), x)] 882.30/297.07 882.30/297.07 [+(x, 0())] = [1] x + [0] 882.30/297.07 >= [1] x + [0] 882.30/297.07 = [x] 882.30/297.07 882.30/297.07 [+(x, s(y))] = [1] x + [0] 882.30/297.07 >= [1] x + [0] 882.30/297.07 = [s(+(x, y))] 882.30/297.07 882.30/297.07 882.30/297.07 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 882.30/297.07 882.30/297.07 We are left with following problem, upon which TcT provides the 882.30/297.07 certificate MAYBE. 882.30/297.07 882.30/297.07 Strict Trs: { +(x, s(y)) -> s(+(x, y)) } 882.30/297.07 Weak Trs: 882.30/297.07 { fib(0()) -> 0() 882.30/297.07 , fib(s(0())) -> s(0()) 882.30/297.07 , fib(s(s(x))) -> sp(g(x)) 882.30/297.07 , fib(s(s(0()))) -> s(0()) 882.30/297.07 , sp(pair(x, y)) -> +(x, y) 882.30/297.07 , g(0()) -> pair(s(0()), 0()) 882.30/297.07 , g(s(x)) -> np(g(x)) 882.30/297.07 , g(s(0())) -> pair(s(0()), s(0())) 882.30/297.07 , np(pair(x, y)) -> pair(+(x, y), x) 882.30/297.07 , +(x, 0()) -> x } 882.30/297.07 Obligation: 882.30/297.07 innermost runtime complexity 882.30/297.07 Answer: 882.30/297.07 MAYBE 882.30/297.07 882.30/297.07 None of the processors succeeded. 882.30/297.07 882.30/297.07 Details of failed attempt(s): 882.30/297.07 ----------------------------- 882.30/297.07 1) 'empty' failed due to the following reason: 882.30/297.07 882.30/297.07 Empty strict component of the problem is NOT empty. 882.30/297.07 882.30/297.07 2) 'With Problem ...' failed due to the following reason: 882.30/297.07 882.30/297.08 None of the processors succeeded. 882.30/297.08 882.30/297.08 Details of failed attempt(s): 882.30/297.08 ----------------------------- 882.30/297.08 1) 'empty' failed due to the following reason: 882.30/297.08 882.30/297.08 Empty strict component of the problem is NOT empty. 882.30/297.08 882.30/297.08 2) 'Fastest' failed due to the following reason: 882.30/297.08 882.30/297.08 None of the processors succeeded. 882.30/297.08 882.30/297.08 Details of failed attempt(s): 882.30/297.08 ----------------------------- 882.30/297.08 1) 'With Problem ...' failed due to the following reason: 882.30/297.08 882.30/297.08 None of the processors succeeded. 882.30/297.08 882.30/297.08 Details of failed attempt(s): 882.30/297.08 ----------------------------- 882.30/297.08 1) 'empty' failed due to the following reason: 882.30/297.08 882.30/297.08 Empty strict component of the problem is NOT empty. 882.30/297.08 882.30/297.08 2) 'With Problem ...' failed due to the following reason: 882.30/297.08 882.30/297.08 None of the processors succeeded. 882.30/297.08 882.30/297.08 Details of failed attempt(s): 882.30/297.08 ----------------------------- 882.30/297.08 1) 'empty' failed due to the following reason: 882.30/297.08 882.30/297.08 Empty strict component of the problem is NOT empty. 882.30/297.08 882.30/297.08 2) 'With Problem ...' failed due to the following reason: 882.30/297.08 882.30/297.08 None of the processors succeeded. 882.30/297.08 882.30/297.08 Details of failed attempt(s): 882.30/297.08 ----------------------------- 882.30/297.08 1) 'empty' failed due to the following reason: 882.30/297.08 882.30/297.08 Empty strict component of the problem is NOT empty. 882.30/297.08 882.30/297.08 2) 'With Problem ...' failed due to the following reason: 882.30/297.08 882.30/297.08 Empty strict component of the problem is NOT empty. 882.30/297.08 882.30/297.08 882.30/297.08 882.30/297.08 882.30/297.08 2) 'With Problem ...' failed due to the following reason: 882.30/297.08 882.30/297.08 None of the processors succeeded. 882.30/297.08 882.30/297.08 Details of failed attempt(s): 882.30/297.08 ----------------------------- 882.30/297.08 1) 'empty' failed due to the following reason: 882.30/297.08 882.30/297.08 Empty strict component of the problem is NOT empty. 882.30/297.08 882.30/297.08 2) 'With Problem ...' failed due to the following reason: 882.30/297.08 882.30/297.08 Empty strict component of the problem is NOT empty. 882.30/297.08 882.30/297.08 882.30/297.08 882.30/297.08 882.30/297.08 882.30/297.08 2) 'Best' failed due to the following reason: 882.30/297.08 882.30/297.08 None of the processors succeeded. 882.30/297.08 882.30/297.08 Details of failed attempt(s): 882.30/297.08 ----------------------------- 882.30/297.08 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 882.30/297.08 following reason: 882.30/297.08 882.30/297.08 The input cannot be shown compatible 882.30/297.08 882.30/297.08 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 882.30/297.08 to the following reason: 882.30/297.08 882.30/297.08 The input cannot be shown compatible 882.30/297.08 882.30/297.08 882.30/297.08 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 882.30/297.08 failed due to the following reason: 882.30/297.08 882.30/297.08 None of the processors succeeded. 882.30/297.08 882.30/297.08 Details of failed attempt(s): 882.30/297.08 ----------------------------- 882.30/297.08 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 882.30/297.08 failed due to the following reason: 882.30/297.08 882.30/297.08 match-boundness of the problem could not be verified. 882.30/297.08 882.30/297.08 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 882.30/297.08 failed due to the following reason: 882.30/297.08 882.30/297.08 match-boundness of the problem could not be verified. 882.30/297.08 882.30/297.08 882.30/297.08 882.30/297.08 882.30/297.08 882.30/297.08 Arrrr.. 882.56/297.13 EOF