MAYBE 715.97/297.02 MAYBE 715.97/297.02 715.97/297.02 We are left with following problem, upon which TcT provides the 715.97/297.02 certificate MAYBE. 715.97/297.02 715.97/297.02 Strict Trs: 715.97/297.02 { fac(0()) -> 1() 715.97/297.02 , fac(0()) -> s(0()) 715.97/297.02 , fac(s(x)) -> *(s(x), fac(x)) 715.97/297.02 , 1() -> s(0()) 715.97/297.02 , *(x, 0()) -> 0() 715.97/297.02 , *(x, s(y)) -> +(*(x, y), x) 715.97/297.02 , floop(0(), y) -> y 715.97/297.02 , floop(s(x), y) -> floop(x, *(s(x), y)) 715.97/297.02 , +(x, 0()) -> x 715.97/297.02 , +(x, s(y)) -> s(+(x, y)) } 715.97/297.02 Obligation: 715.97/297.02 innermost runtime complexity 715.97/297.02 Answer: 715.97/297.02 MAYBE 715.97/297.02 715.97/297.02 None of the processors succeeded. 715.97/297.02 715.97/297.02 Details of failed attempt(s): 715.97/297.02 ----------------------------- 715.97/297.02 1) 'empty' failed due to the following reason: 715.97/297.02 715.97/297.02 Empty strict component of the problem is NOT empty. 715.97/297.02 715.97/297.02 2) 'Best' failed due to the following reason: 715.97/297.02 715.97/297.02 None of the processors succeeded. 715.97/297.02 715.97/297.02 Details of failed attempt(s): 715.97/297.02 ----------------------------- 715.97/297.02 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 715.97/297.02 following reason: 715.97/297.02 715.97/297.02 Computation stopped due to timeout after 297.0 seconds. 715.97/297.02 715.97/297.02 2) 'Best' failed due to the following reason: 715.97/297.02 715.97/297.02 None of the processors succeeded. 715.97/297.02 715.97/297.02 Details of failed attempt(s): 715.97/297.02 ----------------------------- 715.97/297.02 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 715.97/297.02 seconds)' failed due to the following reason: 715.97/297.02 715.97/297.02 The weightgap principle applies (using the following nonconstant 715.97/297.02 growth matrix-interpretation) 715.97/297.02 715.97/297.02 The following argument positions are usable: 715.97/297.02 Uargs(s) = {1}, Uargs(*) = {2}, Uargs(floop) = {2}, Uargs(+) = {1} 715.97/297.02 715.97/297.02 TcT has computed the following matrix interpretation satisfying 715.97/297.02 not(EDA) and not(IDA(1)). 715.97/297.02 715.97/297.02 [fac](x1) = [0] 715.97/297.02 715.97/297.02 [0] = [0] 715.97/297.02 715.97/297.02 [1] = [7] 715.97/297.02 715.97/297.02 [s](x1) = [1] x1 + [0] 715.97/297.02 715.97/297.02 [*](x1, x2) = [1] x2 + [0] 715.97/297.02 715.97/297.02 [floop](x1, x2) = [1] x2 + [0] 715.97/297.02 715.97/297.02 [+](x1, x2) = [1] x1 + [0] 715.97/297.02 715.97/297.02 The order satisfies the following ordering constraints: 715.97/297.02 715.97/297.02 [fac(0())] = [0] 715.97/297.02 ? [7] 715.97/297.02 = [1()] 715.97/297.02 715.97/297.02 [fac(0())] = [0] 715.97/297.02 >= [0] 715.97/297.02 = [s(0())] 715.97/297.02 715.97/297.02 [fac(s(x))] = [0] 715.97/297.02 >= [0] 715.97/297.02 = [*(s(x), fac(x))] 715.97/297.02 715.97/297.02 [1()] = [7] 715.97/297.02 > [0] 715.97/297.02 = [s(0())] 715.97/297.02 715.97/297.02 [*(x, 0())] = [0] 715.97/297.02 >= [0] 715.97/297.02 = [0()] 715.97/297.02 715.97/297.02 [*(x, s(y))] = [1] y + [0] 715.97/297.02 >= [1] y + [0] 715.97/297.02 = [+(*(x, y), x)] 715.97/297.02 715.97/297.02 [floop(0(), y)] = [1] y + [0] 715.97/297.02 >= [1] y + [0] 715.97/297.02 = [y] 715.97/297.02 715.97/297.02 [floop(s(x), y)] = [1] y + [0] 715.97/297.02 >= [1] y + [0] 715.97/297.02 = [floop(x, *(s(x), y))] 715.97/297.02 715.97/297.02 [+(x, 0())] = [1] x + [0] 715.97/297.02 >= [1] x + [0] 715.97/297.02 = [x] 715.97/297.02 715.97/297.02 [+(x, s(y))] = [1] x + [0] 715.97/297.02 >= [1] x + [0] 715.97/297.02 = [s(+(x, y))] 715.97/297.02 715.97/297.02 715.97/297.02 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 715.97/297.02 715.97/297.02 We are left with following problem, upon which TcT provides the 715.97/297.02 certificate MAYBE. 715.97/297.02 715.97/297.02 Strict Trs: 715.97/297.02 { fac(0()) -> 1() 715.97/297.02 , fac(0()) -> s(0()) 715.97/297.02 , fac(s(x)) -> *(s(x), fac(x)) 715.97/297.02 , *(x, 0()) -> 0() 715.97/297.02 , *(x, s(y)) -> +(*(x, y), x) 715.97/297.02 , floop(0(), y) -> y 715.97/297.02 , floop(s(x), y) -> floop(x, *(s(x), y)) 715.97/297.02 , +(x, 0()) -> x 715.97/297.02 , +(x, s(y)) -> s(+(x, y)) } 715.97/297.02 Weak Trs: { 1() -> s(0()) } 715.97/297.02 Obligation: 715.97/297.02 innermost runtime complexity 715.97/297.02 Answer: 715.97/297.02 MAYBE 715.97/297.02 715.97/297.02 The weightgap principle applies (using the following nonconstant 715.97/297.02 growth matrix-interpretation) 715.97/297.02 715.97/297.02 The following argument positions are usable: 715.97/297.02 Uargs(s) = {1}, Uargs(*) = {2}, Uargs(floop) = {2}, Uargs(+) = {1} 715.97/297.02 715.97/297.02 TcT has computed the following matrix interpretation satisfying 715.97/297.02 not(EDA) and not(IDA(1)). 715.97/297.02 715.97/297.02 [fac](x1) = [0] 715.97/297.02 715.97/297.02 [0] = [1] 715.97/297.02 715.97/297.02 [1] = [7] 715.97/297.02 715.97/297.02 [s](x1) = [1] x1 + [0] 715.97/297.02 715.97/297.02 [*](x1, x2) = [1] x2 + [0] 715.97/297.02 715.97/297.02 [floop](x1, x2) = [1] x1 + [1] x2 + [0] 715.97/297.02 715.97/297.02 [+](x1, x2) = [1] x1 + [0] 715.97/297.02 715.97/297.02 The order satisfies the following ordering constraints: 715.97/297.02 715.97/297.02 [fac(0())] = [0] 715.97/297.02 ? [7] 715.97/297.02 = [1()] 715.97/297.02 715.97/297.02 [fac(0())] = [0] 715.97/297.02 ? [1] 715.97/297.02 = [s(0())] 715.97/297.02 715.97/297.02 [fac(s(x))] = [0] 715.97/297.02 >= [0] 715.97/297.02 = [*(s(x), fac(x))] 715.97/297.02 715.97/297.02 [1()] = [7] 715.97/297.02 > [1] 715.97/297.02 = [s(0())] 715.97/297.02 715.97/297.02 [*(x, 0())] = [1] 715.97/297.02 >= [1] 715.97/297.02 = [0()] 715.97/297.02 715.97/297.02 [*(x, s(y))] = [1] y + [0] 715.97/297.02 >= [1] y + [0] 715.97/297.02 = [+(*(x, y), x)] 715.97/297.02 715.97/297.02 [floop(0(), y)] = [1] y + [1] 715.97/297.02 > [1] y + [0] 715.97/297.02 = [y] 715.97/297.02 715.97/297.02 [floop(s(x), y)] = [1] x + [1] y + [0] 715.97/297.02 >= [1] x + [1] y + [0] 715.97/297.02 = [floop(x, *(s(x), y))] 715.97/297.02 715.97/297.02 [+(x, 0())] = [1] x + [0] 715.97/297.02 >= [1] x + [0] 715.97/297.02 = [x] 715.97/297.02 715.97/297.02 [+(x, s(y))] = [1] x + [0] 715.97/297.02 >= [1] x + [0] 715.97/297.02 = [s(+(x, y))] 715.97/297.02 715.97/297.02 715.97/297.02 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 715.97/297.02 715.97/297.02 We are left with following problem, upon which TcT provides the 715.97/297.02 certificate MAYBE. 715.97/297.02 715.97/297.02 Strict Trs: 715.97/297.02 { fac(0()) -> 1() 715.97/297.02 , fac(0()) -> s(0()) 715.97/297.02 , fac(s(x)) -> *(s(x), fac(x)) 715.97/297.02 , *(x, 0()) -> 0() 715.97/297.02 , *(x, s(y)) -> +(*(x, y), x) 715.97/297.02 , floop(s(x), y) -> floop(x, *(s(x), y)) 715.97/297.02 , +(x, 0()) -> x 715.97/297.02 , +(x, s(y)) -> s(+(x, y)) } 715.97/297.02 Weak Trs: 715.97/297.02 { 1() -> s(0()) 715.97/297.02 , floop(0(), y) -> y } 715.97/297.02 Obligation: 715.97/297.02 innermost runtime complexity 715.97/297.02 Answer: 715.97/297.02 MAYBE 715.97/297.02 715.97/297.02 The weightgap principle applies (using the following nonconstant 715.97/297.02 growth matrix-interpretation) 715.97/297.02 715.97/297.02 The following argument positions are usable: 715.97/297.02 Uargs(s) = {1}, Uargs(*) = {2}, Uargs(floop) = {2}, Uargs(+) = {1} 715.97/297.02 715.97/297.02 TcT has computed the following matrix interpretation satisfying 715.97/297.02 not(EDA) and not(IDA(1)). 715.97/297.02 715.97/297.02 [fac](x1) = [1] x1 + [7] 715.97/297.02 715.97/297.02 [0] = [0] 715.97/297.02 715.97/297.02 [1] = [7] 715.97/297.02 715.97/297.02 [s](x1) = [1] x1 + [7] 715.97/297.02 715.97/297.02 [*](x1, x2) = [1] x2 + [7] 715.97/297.02 715.97/297.02 [floop](x1, x2) = [1] x1 + [1] x2 + [7] 715.97/297.02 715.97/297.02 [+](x1, x2) = [1] x1 + [3] 715.97/297.02 715.97/297.02 The order satisfies the following ordering constraints: 715.97/297.02 715.97/297.02 [fac(0())] = [7] 715.97/297.02 >= [7] 715.97/297.02 = [1()] 715.97/297.02 715.97/297.02 [fac(0())] = [7] 715.97/297.02 >= [7] 715.97/297.02 = [s(0())] 715.97/297.02 715.97/297.02 [fac(s(x))] = [1] x + [14] 715.97/297.02 >= [1] x + [14] 715.97/297.02 = [*(s(x), fac(x))] 715.97/297.02 715.97/297.02 [1()] = [7] 715.97/297.02 >= [7] 715.97/297.02 = [s(0())] 715.97/297.02 715.97/297.02 [*(x, 0())] = [7] 715.97/297.02 > [0] 715.97/297.02 = [0()] 715.97/297.02 715.97/297.02 [*(x, s(y))] = [1] y + [14] 715.97/297.02 > [1] y + [10] 715.97/297.02 = [+(*(x, y), x)] 715.97/297.02 715.97/297.02 [floop(0(), y)] = [1] y + [7] 715.97/297.02 > [1] y + [0] 715.97/297.02 = [y] 715.97/297.02 715.97/297.02 [floop(s(x), y)] = [1] x + [1] y + [14] 715.97/297.02 >= [1] x + [1] y + [14] 715.97/297.02 = [floop(x, *(s(x), y))] 715.97/297.02 715.97/297.02 [+(x, 0())] = [1] x + [3] 715.97/297.02 > [1] x + [0] 715.97/297.02 = [x] 715.97/297.02 715.97/297.02 [+(x, s(y))] = [1] x + [3] 715.97/297.02 ? [1] x + [10] 715.97/297.02 = [s(+(x, y))] 715.97/297.02 715.97/297.02 715.97/297.02 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 715.97/297.02 715.97/297.02 We are left with following problem, upon which TcT provides the 715.97/297.02 certificate MAYBE. 715.97/297.02 715.97/297.02 Strict Trs: 715.97/297.02 { fac(0()) -> 1() 715.97/297.02 , fac(0()) -> s(0()) 715.97/297.02 , fac(s(x)) -> *(s(x), fac(x)) 715.97/297.02 , floop(s(x), y) -> floop(x, *(s(x), y)) 715.97/297.02 , +(x, s(y)) -> s(+(x, y)) } 715.97/297.02 Weak Trs: 715.97/297.02 { 1() -> s(0()) 715.97/297.02 , *(x, 0()) -> 0() 715.97/297.02 , *(x, s(y)) -> +(*(x, y), x) 715.97/297.02 , floop(0(), y) -> y 715.97/297.02 , +(x, 0()) -> x } 715.97/297.02 Obligation: 715.97/297.02 innermost runtime complexity 715.97/297.02 Answer: 715.97/297.02 MAYBE 715.97/297.02 715.97/297.02 The weightgap principle applies (using the following nonconstant 715.97/297.02 growth matrix-interpretation) 715.97/297.02 715.97/297.02 The following argument positions are usable: 715.97/297.02 Uargs(s) = {1}, Uargs(*) = {2}, Uargs(floop) = {2}, Uargs(+) = {1} 715.97/297.02 715.97/297.02 TcT has computed the following matrix interpretation satisfying 715.97/297.02 not(EDA) and not(IDA(1)). 715.97/297.02 715.97/297.02 [fac](x1) = [0] 715.97/297.02 715.97/297.02 [0] = [0] 715.97/297.02 715.97/297.02 [1] = [7] 715.97/297.02 715.97/297.02 [s](x1) = [1] x1 + [4] 715.97/297.02 715.97/297.02 [*](x1, x2) = [1] x2 + [0] 715.97/297.02 715.97/297.02 [floop](x1, x2) = [1] x1 + [1] x2 + [0] 715.97/297.02 715.97/297.02 [+](x1, x2) = [1] x1 + [0] 715.97/297.02 715.97/297.02 The order satisfies the following ordering constraints: 715.97/297.02 715.97/297.02 [fac(0())] = [0] 715.97/297.02 ? [7] 715.97/297.02 = [1()] 715.97/297.02 715.97/297.02 [fac(0())] = [0] 715.97/297.02 ? [4] 715.97/297.02 = [s(0())] 715.97/297.02 715.97/297.02 [fac(s(x))] = [0] 715.97/297.02 >= [0] 715.97/297.02 = [*(s(x), fac(x))] 715.97/297.02 715.97/297.02 [1()] = [7] 715.97/297.02 > [4] 715.97/297.02 = [s(0())] 715.97/297.02 715.97/297.02 [*(x, 0())] = [0] 715.97/297.02 >= [0] 715.97/297.02 = [0()] 715.97/297.02 715.97/297.02 [*(x, s(y))] = [1] y + [4] 715.97/297.02 > [1] y + [0] 715.97/297.02 = [+(*(x, y), x)] 715.97/297.02 715.97/297.02 [floop(0(), y)] = [1] y + [0] 715.97/297.02 >= [1] y + [0] 715.97/297.02 = [y] 715.97/297.02 715.97/297.02 [floop(s(x), y)] = [1] x + [1] y + [4] 715.97/297.02 > [1] x + [1] y + [0] 715.97/297.02 = [floop(x, *(s(x), y))] 715.97/297.02 715.97/297.02 [+(x, 0())] = [1] x + [0] 715.97/297.02 >= [1] x + [0] 715.97/297.02 = [x] 715.97/297.02 715.97/297.02 [+(x, s(y))] = [1] x + [0] 715.97/297.02 ? [1] x + [4] 715.97/297.02 = [s(+(x, y))] 715.97/297.02 715.97/297.02 715.97/297.02 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 715.97/297.02 715.97/297.02 We are left with following problem, upon which TcT provides the 715.97/297.02 certificate MAYBE. 715.97/297.02 715.97/297.02 Strict Trs: 715.97/297.02 { fac(0()) -> 1() 715.97/297.02 , fac(0()) -> s(0()) 715.97/297.02 , fac(s(x)) -> *(s(x), fac(x)) 715.97/297.02 , +(x, s(y)) -> s(+(x, y)) } 715.97/297.02 Weak Trs: 715.97/297.02 { 1() -> s(0()) 715.97/297.02 , *(x, 0()) -> 0() 715.97/297.02 , *(x, s(y)) -> +(*(x, y), x) 715.97/297.02 , floop(0(), y) -> y 715.97/297.02 , floop(s(x), y) -> floop(x, *(s(x), y)) 715.97/297.02 , +(x, 0()) -> x } 715.97/297.02 Obligation: 715.97/297.02 innermost runtime complexity 715.97/297.02 Answer: 715.97/297.02 MAYBE 715.97/297.02 715.97/297.02 The weightgap principle applies (using the following nonconstant 715.97/297.02 growth matrix-interpretation) 715.97/297.02 715.97/297.02 The following argument positions are usable: 715.97/297.02 Uargs(s) = {1}, Uargs(*) = {2}, Uargs(floop) = {2}, Uargs(+) = {1} 715.97/297.02 715.97/297.02 TcT has computed the following matrix interpretation satisfying 715.97/297.02 not(EDA) and not(IDA(1)). 715.97/297.02 715.97/297.02 [fac](x1) = [1] x1 + [0] 715.97/297.02 715.97/297.02 [0] = [0] 715.97/297.02 715.97/297.02 [1] = [7] 715.97/297.02 715.97/297.02 [s](x1) = [1] x1 + [4] 715.97/297.02 715.97/297.02 [*](x1, x2) = [1] x2 + [0] 715.97/297.02 715.97/297.02 [floop](x1, x2) = [1] x1 + [1] x2 + [5] 715.97/297.02 715.97/297.02 [+](x1, x2) = [1] x1 + [0] 715.97/297.02 715.97/297.02 The order satisfies the following ordering constraints: 715.97/297.02 715.97/297.02 [fac(0())] = [0] 715.97/297.02 ? [7] 715.97/297.02 = [1()] 715.97/297.02 715.97/297.02 [fac(0())] = [0] 715.97/297.02 ? [4] 715.97/297.02 = [s(0())] 715.97/297.02 715.97/297.02 [fac(s(x))] = [1] x + [4] 715.97/297.02 > [1] x + [0] 715.97/297.02 = [*(s(x), fac(x))] 715.97/297.02 715.97/297.02 [1()] = [7] 715.97/297.02 > [4] 715.97/297.02 = [s(0())] 715.97/297.02 715.97/297.02 [*(x, 0())] = [0] 715.97/297.02 >= [0] 715.97/297.02 = [0()] 715.97/297.02 715.97/297.02 [*(x, s(y))] = [1] y + [4] 715.97/297.02 > [1] y + [0] 715.97/297.02 = [+(*(x, y), x)] 715.97/297.02 715.97/297.02 [floop(0(), y)] = [1] y + [5] 715.97/297.02 > [1] y + [0] 715.97/297.02 = [y] 715.97/297.02 715.97/297.02 [floop(s(x), y)] = [1] x + [1] y + [9] 715.97/297.02 > [1] x + [1] y + [5] 715.97/297.02 = [floop(x, *(s(x), y))] 715.97/297.02 715.97/297.02 [+(x, 0())] = [1] x + [0] 715.97/297.02 >= [1] x + [0] 715.97/297.02 = [x] 715.97/297.02 715.97/297.02 [+(x, s(y))] = [1] x + [0] 715.97/297.02 ? [1] x + [4] 715.97/297.02 = [s(+(x, y))] 715.97/297.02 715.97/297.02 715.97/297.02 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 715.97/297.02 715.97/297.02 We are left with following problem, upon which TcT provides the 715.97/297.02 certificate MAYBE. 715.97/297.02 715.97/297.02 Strict Trs: 715.97/297.02 { fac(0()) -> 1() 715.97/297.02 , fac(0()) -> s(0()) 715.97/297.02 , +(x, s(y)) -> s(+(x, y)) } 715.97/297.02 Weak Trs: 715.97/297.02 { fac(s(x)) -> *(s(x), fac(x)) 715.97/297.02 , 1() -> s(0()) 715.97/297.02 , *(x, 0()) -> 0() 715.97/297.02 , *(x, s(y)) -> +(*(x, y), x) 715.97/297.02 , floop(0(), y) -> y 715.97/297.02 , floop(s(x), y) -> floop(x, *(s(x), y)) 715.97/297.02 , +(x, 0()) -> x } 715.97/297.02 Obligation: 715.97/297.02 innermost runtime complexity 715.97/297.02 Answer: 715.97/297.02 MAYBE 715.97/297.02 715.97/297.02 The weightgap principle applies (using the following nonconstant 715.97/297.02 growth matrix-interpretation) 715.97/297.02 715.97/297.02 The following argument positions are usable: 715.97/297.02 Uargs(s) = {1}, Uargs(*) = {2}, Uargs(floop) = {2}, Uargs(+) = {1} 715.97/297.02 715.97/297.02 TcT has computed the following matrix interpretation satisfying 715.97/297.02 not(EDA) and not(IDA(1)). 715.97/297.02 715.97/297.02 [fac](x1) = [1] x1 + [6] 715.97/297.02 715.97/297.02 [0] = [0] 715.97/297.02 715.97/297.02 [1] = [7] 715.97/297.02 715.97/297.02 [s](x1) = [1] x1 + [2] 715.97/297.02 715.97/297.02 [*](x1, x2) = [1] x2 + [0] 715.97/297.02 715.97/297.02 [floop](x1, x2) = [1] x2 + [5] 715.97/297.02 715.97/297.02 [+](x1, x2) = [1] x1 + [2] 715.97/297.02 715.97/297.02 The order satisfies the following ordering constraints: 715.97/297.02 715.97/297.02 [fac(0())] = [6] 715.97/297.02 ? [7] 715.97/297.02 = [1()] 715.97/297.02 715.97/297.02 [fac(0())] = [6] 715.97/297.02 > [2] 715.97/297.02 = [s(0())] 715.97/297.02 715.97/297.02 [fac(s(x))] = [1] x + [8] 715.97/297.02 > [1] x + [6] 715.97/297.02 = [*(s(x), fac(x))] 715.97/297.02 715.97/297.02 [1()] = [7] 715.97/297.02 > [2] 715.97/297.02 = [s(0())] 715.97/297.02 715.97/297.02 [*(x, 0())] = [0] 715.97/297.02 >= [0] 715.97/297.02 = [0()] 715.97/297.02 715.97/297.02 [*(x, s(y))] = [1] y + [2] 715.97/297.02 >= [1] y + [2] 715.97/297.02 = [+(*(x, y), x)] 715.97/297.02 715.97/297.02 [floop(0(), y)] = [1] y + [5] 715.97/297.02 > [1] y + [0] 715.97/297.02 = [y] 715.97/297.02 715.97/297.02 [floop(s(x), y)] = [1] y + [5] 715.97/297.02 >= [1] y + [5] 715.97/297.02 = [floop(x, *(s(x), y))] 715.97/297.02 715.97/297.02 [+(x, 0())] = [1] x + [2] 715.97/297.02 > [1] x + [0] 715.97/297.02 = [x] 715.97/297.02 715.97/297.02 [+(x, s(y))] = [1] x + [2] 715.97/297.02 ? [1] x + [4] 715.97/297.02 = [s(+(x, y))] 715.97/297.02 715.97/297.02 715.97/297.02 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 715.97/297.02 715.97/297.02 We are left with following problem, upon which TcT provides the 715.97/297.02 certificate MAYBE. 715.97/297.02 715.97/297.02 Strict Trs: 715.97/297.02 { fac(0()) -> 1() 715.97/297.02 , +(x, s(y)) -> s(+(x, y)) } 715.97/297.02 Weak Trs: 715.97/297.02 { fac(0()) -> s(0()) 715.97/297.02 , fac(s(x)) -> *(s(x), fac(x)) 715.97/297.02 , 1() -> s(0()) 715.97/297.02 , *(x, 0()) -> 0() 715.97/297.02 , *(x, s(y)) -> +(*(x, y), x) 715.97/297.02 , floop(0(), y) -> y 715.97/297.02 , floop(s(x), y) -> floop(x, *(s(x), y)) 715.97/297.02 , +(x, 0()) -> x } 715.97/297.02 Obligation: 715.97/297.02 innermost runtime complexity 715.97/297.02 Answer: 715.97/297.02 MAYBE 715.97/297.02 715.97/297.02 The weightgap principle applies (using the following nonconstant 715.97/297.02 growth matrix-interpretation) 715.97/297.02 715.97/297.02 The following argument positions are usable: 715.97/297.02 Uargs(s) = {1}, Uargs(*) = {2}, Uargs(floop) = {2}, Uargs(+) = {1} 715.97/297.02 715.97/297.02 TcT has computed the following matrix interpretation satisfying 715.97/297.02 not(EDA) and not(IDA(1)). 715.97/297.02 715.97/297.02 [fac](x1) = [1] x1 + [4] 715.97/297.02 715.97/297.02 [0] = [4] 715.97/297.02 715.97/297.02 [1] = [7] 715.97/297.02 715.97/297.02 [s](x1) = [1] x1 + [0] 715.97/297.02 715.97/297.02 [*](x1, x2) = [1] x2 + [0] 715.97/297.02 715.97/297.02 [floop](x1, x2) = [1] x1 + [1] x2 + [5] 715.97/297.02 715.97/297.02 [+](x1, x2) = [1] x1 + [0] 715.97/297.02 715.97/297.02 The order satisfies the following ordering constraints: 715.97/297.02 715.97/297.02 [fac(0())] = [8] 715.97/297.02 > [7] 715.97/297.02 = [1()] 715.97/297.02 715.97/297.02 [fac(0())] = [8] 715.97/297.02 > [4] 715.97/297.02 = [s(0())] 715.97/297.02 715.97/297.02 [fac(s(x))] = [1] x + [4] 715.97/297.02 >= [1] x + [4] 715.97/297.02 = [*(s(x), fac(x))] 715.97/297.02 715.97/297.02 [1()] = [7] 715.97/297.02 > [4] 715.97/297.02 = [s(0())] 715.97/297.02 715.97/297.02 [*(x, 0())] = [4] 715.97/297.02 >= [4] 715.97/297.02 = [0()] 715.97/297.02 715.97/297.02 [*(x, s(y))] = [1] y + [0] 715.97/297.02 >= [1] y + [0] 715.97/297.02 = [+(*(x, y), x)] 715.97/297.02 715.97/297.02 [floop(0(), y)] = [1] y + [9] 715.97/297.02 > [1] y + [0] 715.97/297.02 = [y] 715.97/297.02 715.97/297.02 [floop(s(x), y)] = [1] x + [1] y + [5] 715.97/297.02 >= [1] x + [1] y + [5] 715.97/297.02 = [floop(x, *(s(x), y))] 715.97/297.02 715.97/297.02 [+(x, 0())] = [1] x + [0] 715.97/297.02 >= [1] x + [0] 715.97/297.02 = [x] 715.97/297.02 715.97/297.02 [+(x, s(y))] = [1] x + [0] 715.97/297.02 >= [1] x + [0] 715.97/297.02 = [s(+(x, y))] 715.97/297.02 715.97/297.02 715.97/297.02 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 715.97/297.02 715.97/297.02 We are left with following problem, upon which TcT provides the 715.97/297.02 certificate MAYBE. 715.97/297.02 715.97/297.02 Strict Trs: { +(x, s(y)) -> s(+(x, y)) } 715.97/297.02 Weak Trs: 715.97/297.02 { fac(0()) -> 1() 715.97/297.02 , fac(0()) -> s(0()) 715.97/297.02 , fac(s(x)) -> *(s(x), fac(x)) 715.97/297.02 , 1() -> s(0()) 715.97/297.02 , *(x, 0()) -> 0() 715.97/297.02 , *(x, s(y)) -> +(*(x, y), x) 715.97/297.02 , floop(0(), y) -> y 715.97/297.02 , floop(s(x), y) -> floop(x, *(s(x), y)) 715.97/297.02 , +(x, 0()) -> x } 715.97/297.02 Obligation: 715.97/297.02 innermost runtime complexity 715.97/297.02 Answer: 715.97/297.02 MAYBE 715.97/297.02 715.97/297.02 None of the processors succeeded. 715.97/297.02 715.97/297.02 Details of failed attempt(s): 715.97/297.02 ----------------------------- 715.97/297.02 1) 'empty' failed due to the following reason: 715.97/297.02 715.97/297.02 Empty strict component of the problem is NOT empty. 715.97/297.02 715.97/297.02 2) 'With Problem ...' failed due to the following reason: 715.97/297.02 715.97/297.02 None of the processors succeeded. 715.97/297.02 715.97/297.02 Details of failed attempt(s): 715.97/297.02 ----------------------------- 715.97/297.02 1) 'empty' failed due to the following reason: 715.97/297.02 715.97/297.02 Empty strict component of the problem is NOT empty. 715.97/297.02 715.97/297.02 2) 'Fastest' failed due to the following reason: 715.97/297.02 715.97/297.02 None of the processors succeeded. 715.97/297.02 715.97/297.02 Details of failed attempt(s): 715.97/297.02 ----------------------------- 715.97/297.02 1) 'With Problem ...' failed due to the following reason: 715.97/297.02 715.97/297.02 None of the processors succeeded. 715.97/297.02 715.97/297.02 Details of failed attempt(s): 715.97/297.02 ----------------------------- 715.97/297.02 1) 'empty' failed due to the following reason: 715.97/297.02 715.97/297.02 Empty strict component of the problem is NOT empty. 715.97/297.02 715.97/297.02 2) 'With Problem ...' failed due to the following reason: 715.97/297.02 715.97/297.02 Empty strict component of the problem is NOT empty. 715.97/297.02 715.97/297.02 715.97/297.02 2) 'With Problem ...' failed due to the following reason: 715.97/297.02 715.97/297.02 None of the processors succeeded. 715.97/297.02 715.97/297.02 Details of failed attempt(s): 715.97/297.02 ----------------------------- 715.97/297.02 1) 'empty' failed due to the following reason: 715.97/297.02 715.97/297.02 Empty strict component of the problem is NOT empty. 715.97/297.02 715.97/297.02 2) 'With Problem ...' failed due to the following reason: 715.97/297.02 715.97/297.02 None of the processors succeeded. 715.97/297.02 715.97/297.02 Details of failed attempt(s): 715.97/297.02 ----------------------------- 715.97/297.02 1) 'empty' failed due to the following reason: 715.97/297.02 715.97/297.02 Empty strict component of the problem is NOT empty. 715.97/297.02 715.97/297.02 2) 'With Problem ...' failed due to the following reason: 715.97/297.02 715.97/297.02 None of the processors succeeded. 715.97/297.02 715.97/297.02 Details of failed attempt(s): 715.97/297.02 ----------------------------- 715.97/297.02 1) 'empty' failed due to the following reason: 715.97/297.02 715.97/297.02 Empty strict component of the problem is NOT empty. 715.97/297.02 715.97/297.02 2) 'With Problem ...' failed due to the following reason: 715.97/297.02 715.97/297.02 Empty strict component of the problem is NOT empty. 715.97/297.02 715.97/297.02 715.97/297.02 715.97/297.02 715.97/297.02 715.97/297.02 715.97/297.02 715.97/297.02 2) 'Best' failed due to the following reason: 715.97/297.02 715.97/297.02 None of the processors succeeded. 715.97/297.02 715.97/297.02 Details of failed attempt(s): 715.97/297.02 ----------------------------- 715.97/297.02 1) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 715.97/297.02 to the following reason: 715.97/297.02 715.97/297.02 The input cannot be shown compatible 715.97/297.02 715.97/297.02 2) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 715.97/297.02 following reason: 715.97/297.02 715.97/297.02 The input cannot be shown compatible 715.97/297.02 715.97/297.02 715.97/297.02 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 715.97/297.02 failed due to the following reason: 715.97/297.02 715.97/297.02 None of the processors succeeded. 715.97/297.02 715.97/297.02 Details of failed attempt(s): 715.97/297.02 ----------------------------- 715.97/297.02 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 715.97/297.02 failed due to the following reason: 715.97/297.02 715.97/297.02 match-boundness of the problem could not be verified. 715.97/297.02 715.97/297.02 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 715.97/297.02 failed due to the following reason: 715.97/297.02 715.97/297.02 match-boundness of the problem could not be verified. 715.97/297.02 715.97/297.02 715.97/297.02 715.97/297.02 715.97/297.02 715.97/297.02 Arrrr.. 716.09/297.14 EOF