MAYBE 772.48/297.03 MAYBE 772.48/297.03 772.48/297.03 We are left with following problem, upon which TcT provides the 772.48/297.03 certificate MAYBE. 772.48/297.03 772.48/297.03 Strict Trs: 772.48/297.03 { minus(x, x) -> 0() 772.48/297.03 , minus(x, 0()) -> x 772.48/297.03 , minus(0(), x) -> 0() 772.48/297.03 , minus(s(x), s(y)) -> minus(x, y) 772.48/297.03 , le(0(), y) -> true() 772.48/297.03 , le(s(x), 0()) -> false() 772.48/297.03 , le(s(x), s(y)) -> le(x, y) 772.48/297.03 , quot(x, y) -> if_quot(minus(x, y), y, le(y, 0()), le(y, x)) 772.48/297.03 , if_quot(x, y, true(), z) -> divByZeroError() 772.48/297.03 , if_quot(x, y, false(), true()) -> s(quot(x, y)) 772.48/297.03 , if_quot(x, y, false(), false()) -> 0() } 772.48/297.03 Obligation: 772.48/297.03 innermost runtime complexity 772.48/297.03 Answer: 772.48/297.03 MAYBE 772.48/297.03 772.48/297.03 None of the processors succeeded. 772.48/297.03 772.48/297.03 Details of failed attempt(s): 772.48/297.03 ----------------------------- 772.48/297.03 1) 'empty' failed due to the following reason: 772.48/297.03 772.48/297.03 Empty strict component of the problem is NOT empty. 772.48/297.03 772.48/297.03 2) 'Best' failed due to the following reason: 772.48/297.03 772.48/297.03 None of the processors succeeded. 772.48/297.03 772.48/297.03 Details of failed attempt(s): 772.48/297.03 ----------------------------- 772.48/297.03 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 772.48/297.03 following reason: 772.48/297.03 772.48/297.03 Computation stopped due to timeout after 297.0 seconds. 772.48/297.03 772.48/297.03 2) 'Best' failed due to the following reason: 772.48/297.03 772.48/297.03 None of the processors succeeded. 772.48/297.03 772.48/297.03 Details of failed attempt(s): 772.48/297.03 ----------------------------- 772.48/297.03 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 772.48/297.03 seconds)' failed due to the following reason: 772.48/297.03 772.48/297.03 The weightgap principle applies (using the following nonconstant 772.48/297.03 growth matrix-interpretation) 772.48/297.03 772.48/297.03 The following argument positions are usable: 772.48/297.03 Uargs(s) = {1}, Uargs(if_quot) = {1, 3, 4} 772.48/297.03 772.48/297.03 TcT has computed the following matrix interpretation satisfying 772.48/297.03 not(EDA) and not(IDA(1)). 772.48/297.03 772.48/297.03 [minus](x1, x2) = [1] x1 + [0] 772.48/297.03 772.48/297.03 [0] = [1] 772.48/297.03 772.48/297.03 [s](x1) = [1] x1 + [0] 772.48/297.03 772.48/297.03 [le](x1, x2) = [0] 772.48/297.03 772.48/297.03 [true] = [1] 772.48/297.03 772.48/297.03 [false] = [0] 772.48/297.03 772.48/297.03 [quot](x1, x2) = [1] x1 + [0] 772.48/297.03 772.48/297.03 [if_quot](x1, x2, x3, x4) = [1] x1 + [1] x3 + [1] x4 + [0] 772.48/297.03 772.48/297.03 [divByZeroError] = [0] 772.48/297.03 772.48/297.03 The order satisfies the following ordering constraints: 772.48/297.03 772.48/297.03 [minus(x, x)] = [1] x + [0] 772.48/297.03 ? [1] 772.48/297.03 = [0()] 772.48/297.03 772.48/297.03 [minus(x, 0())] = [1] x + [0] 772.48/297.03 >= [1] x + [0] 772.48/297.03 = [x] 772.48/297.03 772.48/297.03 [minus(0(), x)] = [1] 772.48/297.03 >= [1] 772.48/297.03 = [0()] 772.48/297.03 772.48/297.03 [minus(s(x), s(y))] = [1] x + [0] 772.48/297.03 >= [1] x + [0] 772.48/297.03 = [minus(x, y)] 772.48/297.03 772.48/297.03 [le(0(), y)] = [0] 772.48/297.03 ? [1] 772.48/297.03 = [true()] 772.48/297.03 772.48/297.03 [le(s(x), 0())] = [0] 772.48/297.03 >= [0] 772.48/297.03 = [false()] 772.48/297.03 772.48/297.03 [le(s(x), s(y))] = [0] 772.48/297.03 >= [0] 772.48/297.03 = [le(x, y)] 772.48/297.03 772.48/297.03 [quot(x, y)] = [1] x + [0] 772.48/297.03 >= [1] x + [0] 772.48/297.03 = [if_quot(minus(x, y), y, le(y, 0()), le(y, x))] 772.48/297.03 772.48/297.03 [if_quot(x, y, true(), z)] = [1] x + [1] z + [1] 772.48/297.03 > [0] 772.48/297.03 = [divByZeroError()] 772.48/297.03 772.48/297.03 [if_quot(x, y, false(), true())] = [1] x + [1] 772.48/297.03 > [1] x + [0] 772.48/297.03 = [s(quot(x, y))] 772.48/297.03 772.48/297.03 [if_quot(x, y, false(), false())] = [1] x + [0] 772.48/297.03 ? [1] 772.48/297.03 = [0()] 772.48/297.03 772.48/297.03 772.48/297.03 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 772.48/297.03 772.48/297.03 We are left with following problem, upon which TcT provides the 772.48/297.03 certificate MAYBE. 772.48/297.03 772.48/297.03 Strict Trs: 772.48/297.03 { minus(x, x) -> 0() 772.48/297.03 , minus(x, 0()) -> x 772.48/297.03 , minus(0(), x) -> 0() 772.48/297.03 , minus(s(x), s(y)) -> minus(x, y) 772.48/297.03 , le(0(), y) -> true() 772.48/297.03 , le(s(x), 0()) -> false() 772.48/297.03 , le(s(x), s(y)) -> le(x, y) 772.48/297.03 , quot(x, y) -> if_quot(minus(x, y), y, le(y, 0()), le(y, x)) 772.48/297.03 , if_quot(x, y, false(), false()) -> 0() } 772.48/297.03 Weak Trs: 772.48/297.03 { if_quot(x, y, true(), z) -> divByZeroError() 772.48/297.03 , if_quot(x, y, false(), true()) -> s(quot(x, y)) } 772.48/297.03 Obligation: 772.48/297.03 innermost runtime complexity 772.48/297.03 Answer: 772.48/297.03 MAYBE 772.48/297.03 772.48/297.03 The weightgap principle applies (using the following nonconstant 772.48/297.03 growth matrix-interpretation) 772.48/297.03 772.48/297.03 The following argument positions are usable: 772.48/297.03 Uargs(s) = {1}, Uargs(if_quot) = {1, 3, 4} 772.48/297.03 772.48/297.03 TcT has computed the following matrix interpretation satisfying 772.48/297.03 not(EDA) and not(IDA(1)). 772.48/297.03 772.48/297.03 [minus](x1, x2) = [1] x1 + [0] 772.48/297.03 772.48/297.03 [0] = [1] 772.48/297.03 772.48/297.03 [s](x1) = [1] x1 + [0] 772.48/297.03 772.48/297.03 [le](x1, x2) = [0] 772.48/297.03 772.48/297.03 [true] = [4] 772.48/297.03 772.48/297.03 [false] = [4] 772.48/297.03 772.48/297.03 [quot](x1, x2) = [1] x1 + [1] x2 + [0] 772.48/297.03 772.48/297.03 [if_quot](x1, x2, x3, x4) = [1] x1 + [1] x2 + [1] x3 + [1] x4 + [0] 772.48/297.03 772.48/297.03 [divByZeroError] = [4] 772.48/297.03 772.48/297.03 The order satisfies the following ordering constraints: 772.48/297.03 772.48/297.03 [minus(x, x)] = [1] x + [0] 772.48/297.03 ? [1] 772.48/297.03 = [0()] 772.48/297.03 772.48/297.03 [minus(x, 0())] = [1] x + [0] 772.48/297.03 >= [1] x + [0] 772.48/297.03 = [x] 772.48/297.03 772.48/297.03 [minus(0(), x)] = [1] 772.48/297.03 >= [1] 772.48/297.03 = [0()] 772.48/297.03 772.48/297.03 [minus(s(x), s(y))] = [1] x + [0] 772.48/297.03 >= [1] x + [0] 772.48/297.03 = [minus(x, y)] 772.48/297.03 772.48/297.03 [le(0(), y)] = [0] 772.48/297.03 ? [4] 772.48/297.03 = [true()] 772.48/297.03 772.48/297.03 [le(s(x), 0())] = [0] 772.48/297.03 ? [4] 772.48/297.03 = [false()] 772.48/297.03 772.48/297.03 [le(s(x), s(y))] = [0] 772.48/297.03 >= [0] 772.48/297.03 = [le(x, y)] 772.48/297.03 772.48/297.03 [quot(x, y)] = [1] x + [1] y + [0] 772.48/297.03 >= [1] x + [1] y + [0] 772.48/297.03 = [if_quot(minus(x, y), y, le(y, 0()), le(y, x))] 772.48/297.03 772.48/297.03 [if_quot(x, y, true(), z)] = [1] x + [1] y + [1] z + [4] 772.48/297.03 >= [4] 772.48/297.03 = [divByZeroError()] 772.48/297.03 772.48/297.03 [if_quot(x, y, false(), true())] = [1] x + [1] y + [8] 772.48/297.03 > [1] x + [1] y + [0] 772.48/297.03 = [s(quot(x, y))] 772.48/297.03 772.48/297.03 [if_quot(x, y, false(), false())] = [1] x + [1] y + [8] 772.48/297.03 > [1] 772.48/297.03 = [0()] 772.48/297.03 772.48/297.03 772.48/297.03 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 772.48/297.03 772.48/297.03 We are left with following problem, upon which TcT provides the 772.48/297.03 certificate MAYBE. 772.48/297.03 772.48/297.03 Strict Trs: 772.48/297.03 { minus(x, x) -> 0() 772.48/297.03 , minus(x, 0()) -> x 772.48/297.03 , minus(0(), x) -> 0() 772.48/297.03 , minus(s(x), s(y)) -> minus(x, y) 772.48/297.03 , le(0(), y) -> true() 772.48/297.03 , le(s(x), 0()) -> false() 772.48/297.03 , le(s(x), s(y)) -> le(x, y) 772.48/297.03 , quot(x, y) -> if_quot(minus(x, y), y, le(y, 0()), le(y, x)) } 772.48/297.03 Weak Trs: 772.48/297.03 { if_quot(x, y, true(), z) -> divByZeroError() 772.48/297.03 , if_quot(x, y, false(), true()) -> s(quot(x, y)) 772.48/297.03 , if_quot(x, y, false(), false()) -> 0() } 772.48/297.03 Obligation: 772.48/297.03 innermost runtime complexity 772.48/297.03 Answer: 772.48/297.03 MAYBE 772.48/297.03 772.48/297.03 The weightgap principle applies (using the following nonconstant 772.48/297.03 growth matrix-interpretation) 772.48/297.03 772.48/297.03 The following argument positions are usable: 772.48/297.03 Uargs(s) = {1}, Uargs(if_quot) = {1, 3, 4} 772.48/297.03 772.48/297.03 TcT has computed the following matrix interpretation satisfying 772.48/297.03 not(EDA) and not(IDA(1)). 772.48/297.03 772.48/297.03 [minus](x1, x2) = [1] x1 + [0] 772.48/297.03 772.48/297.03 [0] = [3] 772.48/297.03 772.48/297.03 [s](x1) = [1] x1 + [0] 772.48/297.03 772.48/297.03 [le](x1, x2) = [0] 772.48/297.03 772.48/297.03 [true] = [4] 772.48/297.03 772.48/297.03 [false] = [4] 772.48/297.03 772.48/297.03 [quot](x1, x2) = [1] x1 + [4] 772.48/297.03 772.48/297.03 [if_quot](x1, x2, x3, x4) = [1] x1 + [1] x3 + [1] x4 + [0] 772.48/297.03 772.48/297.03 [divByZeroError] = [4] 772.48/297.03 772.48/297.03 The order satisfies the following ordering constraints: 772.48/297.03 772.48/297.03 [minus(x, x)] = [1] x + [0] 772.48/297.03 ? [3] 772.48/297.03 = [0()] 772.48/297.03 772.48/297.03 [minus(x, 0())] = [1] x + [0] 772.48/297.03 >= [1] x + [0] 772.48/297.03 = [x] 772.48/297.03 772.48/297.03 [minus(0(), x)] = [3] 772.48/297.03 >= [3] 772.48/297.03 = [0()] 772.48/297.03 772.48/297.03 [minus(s(x), s(y))] = [1] x + [0] 772.48/297.03 >= [1] x + [0] 772.48/297.03 = [minus(x, y)] 772.48/297.03 772.48/297.03 [le(0(), y)] = [0] 772.48/297.03 ? [4] 772.48/297.03 = [true()] 772.48/297.03 772.48/297.03 [le(s(x), 0())] = [0] 772.48/297.03 ? [4] 772.48/297.03 = [false()] 772.48/297.03 772.48/297.03 [le(s(x), s(y))] = [0] 772.48/297.03 >= [0] 772.48/297.03 = [le(x, y)] 772.48/297.03 772.48/297.03 [quot(x, y)] = [1] x + [4] 772.48/297.03 > [1] x + [0] 772.48/297.03 = [if_quot(minus(x, y), y, le(y, 0()), le(y, x))] 772.48/297.03 772.48/297.03 [if_quot(x, y, true(), z)] = [1] x + [1] z + [4] 772.48/297.03 >= [4] 772.48/297.03 = [divByZeroError()] 772.48/297.03 772.48/297.03 [if_quot(x, y, false(), true())] = [1] x + [8] 772.48/297.03 > [1] x + [4] 772.48/297.03 = [s(quot(x, y))] 772.48/297.03 772.48/297.03 [if_quot(x, y, false(), false())] = [1] x + [8] 772.48/297.03 > [3] 772.48/297.03 = [0()] 772.48/297.03 772.48/297.03 772.48/297.03 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 772.48/297.03 772.48/297.03 We are left with following problem, upon which TcT provides the 772.48/297.03 certificate MAYBE. 772.48/297.03 772.48/297.03 Strict Trs: 772.48/297.03 { minus(x, x) -> 0() 772.48/297.03 , minus(x, 0()) -> x 772.48/297.03 , minus(0(), x) -> 0() 772.48/297.03 , minus(s(x), s(y)) -> minus(x, y) 772.48/297.03 , le(0(), y) -> true() 772.48/297.03 , le(s(x), 0()) -> false() 772.48/297.03 , le(s(x), s(y)) -> le(x, y) } 772.48/297.03 Weak Trs: 772.48/297.03 { quot(x, y) -> if_quot(minus(x, y), y, le(y, 0()), le(y, x)) 772.48/297.03 , if_quot(x, y, true(), z) -> divByZeroError() 772.48/297.03 , if_quot(x, y, false(), true()) -> s(quot(x, y)) 772.48/297.03 , if_quot(x, y, false(), false()) -> 0() } 772.48/297.03 Obligation: 772.48/297.03 innermost runtime complexity 772.48/297.03 Answer: 772.48/297.03 MAYBE 772.48/297.03 772.48/297.03 The weightgap principle applies (using the following nonconstant 772.48/297.03 growth matrix-interpretation) 772.48/297.03 772.48/297.03 The following argument positions are usable: 772.48/297.03 Uargs(s) = {1}, Uargs(if_quot) = {1, 3, 4} 772.48/297.03 772.48/297.03 TcT has computed the following matrix interpretation satisfying 772.48/297.03 not(EDA) and not(IDA(1)). 772.48/297.03 772.48/297.03 [minus](x1, x2) = [1] x1 + [0] 772.48/297.03 772.48/297.03 [0] = [7] 772.48/297.03 772.48/297.03 [s](x1) = [1] x1 + [4] 772.48/297.03 772.48/297.03 [le](x1, x2) = [0] 772.48/297.03 772.48/297.03 [true] = [4] 772.48/297.03 772.48/297.03 [false] = [4] 772.48/297.03 772.48/297.03 [quot](x1, x2) = [1] x1 + [4] 772.48/297.03 772.48/297.03 [if_quot](x1, x2, x3, x4) = [1] x1 + [1] x3 + [1] x4 + [0] 772.48/297.03 772.48/297.03 [divByZeroError] = [4] 772.48/297.03 772.48/297.03 The order satisfies the following ordering constraints: 772.48/297.03 772.48/297.03 [minus(x, x)] = [1] x + [0] 772.48/297.03 ? [7] 772.48/297.03 = [0()] 772.48/297.03 772.48/297.03 [minus(x, 0())] = [1] x + [0] 772.48/297.03 >= [1] x + [0] 772.48/297.03 = [x] 772.48/297.03 772.48/297.03 [minus(0(), x)] = [7] 772.48/297.03 >= [7] 772.48/297.03 = [0()] 772.48/297.03 772.48/297.03 [minus(s(x), s(y))] = [1] x + [4] 772.48/297.03 > [1] x + [0] 772.48/297.03 = [minus(x, y)] 772.48/297.03 772.48/297.03 [le(0(), y)] = [0] 772.48/297.03 ? [4] 772.48/297.03 = [true()] 772.48/297.03 772.48/297.03 [le(s(x), 0())] = [0] 772.48/297.03 ? [4] 772.48/297.03 = [false()] 772.48/297.03 772.48/297.03 [le(s(x), s(y))] = [0] 772.48/297.03 >= [0] 772.48/297.03 = [le(x, y)] 772.48/297.03 772.48/297.03 [quot(x, y)] = [1] x + [4] 772.48/297.03 > [1] x + [0] 772.48/297.03 = [if_quot(minus(x, y), y, le(y, 0()), le(y, x))] 772.48/297.03 772.48/297.03 [if_quot(x, y, true(), z)] = [1] x + [1] z + [4] 772.48/297.03 >= [4] 772.48/297.03 = [divByZeroError()] 772.48/297.03 772.48/297.03 [if_quot(x, y, false(), true())] = [1] x + [8] 772.48/297.03 >= [1] x + [8] 772.48/297.03 = [s(quot(x, y))] 772.48/297.03 772.48/297.03 [if_quot(x, y, false(), false())] = [1] x + [8] 772.48/297.03 > [7] 772.48/297.03 = [0()] 772.48/297.03 772.48/297.03 772.48/297.03 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 772.48/297.03 772.48/297.03 We are left with following problem, upon which TcT provides the 772.48/297.03 certificate MAYBE. 772.48/297.03 772.48/297.03 Strict Trs: 772.48/297.03 { minus(x, x) -> 0() 772.48/297.03 , minus(x, 0()) -> x 772.48/297.03 , minus(0(), x) -> 0() 772.48/297.03 , le(0(), y) -> true() 772.48/297.03 , le(s(x), 0()) -> false() 772.48/297.03 , le(s(x), s(y)) -> le(x, y) } 772.48/297.03 Weak Trs: 772.48/297.03 { minus(s(x), s(y)) -> minus(x, y) 772.48/297.03 , quot(x, y) -> if_quot(minus(x, y), y, le(y, 0()), le(y, x)) 772.48/297.03 , if_quot(x, y, true(), z) -> divByZeroError() 772.48/297.03 , if_quot(x, y, false(), true()) -> s(quot(x, y)) 772.48/297.03 , if_quot(x, y, false(), false()) -> 0() } 772.48/297.03 Obligation: 772.48/297.03 innermost runtime complexity 772.48/297.03 Answer: 772.48/297.03 MAYBE 772.48/297.03 772.48/297.03 The weightgap principle applies (using the following nonconstant 772.48/297.03 growth matrix-interpretation) 772.48/297.03 772.48/297.03 The following argument positions are usable: 772.48/297.03 Uargs(s) = {1}, Uargs(if_quot) = {1, 3, 4} 772.48/297.03 772.48/297.03 TcT has computed the following matrix interpretation satisfying 772.48/297.03 not(EDA) and not(IDA(1)). 772.48/297.03 772.48/297.03 [minus](x1, x2) = [1] x1 + [1] 772.48/297.03 772.48/297.03 [0] = [2] 772.48/297.03 772.48/297.03 [s](x1) = [1] x1 + [1] 772.48/297.03 772.48/297.03 [le](x1, x2) = [0] 772.48/297.03 772.48/297.04 [true] = [4] 772.48/297.04 772.48/297.04 [false] = [4] 772.48/297.04 772.48/297.04 [quot](x1, x2) = [1] x1 + [5] 772.48/297.04 772.48/297.04 [if_quot](x1, x2, x3, x4) = [1] x1 + [1] x3 + [1] x4 + [0] 772.48/297.04 772.48/297.04 [divByZeroError] = [4] 772.48/297.04 772.48/297.04 The order satisfies the following ordering constraints: 772.48/297.04 772.48/297.04 [minus(x, x)] = [1] x + [1] 772.48/297.04 ? [2] 772.48/297.04 = [0()] 772.48/297.04 772.48/297.04 [minus(x, 0())] = [1] x + [1] 772.48/297.04 > [1] x + [0] 772.48/297.04 = [x] 772.48/297.04 772.48/297.04 [minus(0(), x)] = [3] 772.48/297.04 > [2] 772.48/297.04 = [0()] 772.48/297.04 772.48/297.04 [minus(s(x), s(y))] = [1] x + [2] 772.48/297.04 > [1] x + [1] 772.48/297.04 = [minus(x, y)] 772.48/297.04 772.48/297.04 [le(0(), y)] = [0] 772.48/297.04 ? [4] 772.48/297.04 = [true()] 772.48/297.04 772.48/297.04 [le(s(x), 0())] = [0] 772.48/297.04 ? [4] 772.48/297.04 = [false()] 772.48/297.04 772.48/297.04 [le(s(x), s(y))] = [0] 772.48/297.04 >= [0] 772.48/297.04 = [le(x, y)] 772.48/297.04 772.48/297.04 [quot(x, y)] = [1] x + [5] 772.48/297.04 > [1] x + [1] 772.48/297.04 = [if_quot(minus(x, y), y, le(y, 0()), le(y, x))] 772.48/297.04 772.48/297.04 [if_quot(x, y, true(), z)] = [1] x + [1] z + [4] 772.48/297.04 >= [4] 772.48/297.04 = [divByZeroError()] 772.48/297.04 772.48/297.04 [if_quot(x, y, false(), true())] = [1] x + [8] 772.48/297.04 > [1] x + [6] 772.48/297.04 = [s(quot(x, y))] 772.48/297.04 772.48/297.04 [if_quot(x, y, false(), false())] = [1] x + [8] 772.48/297.04 > [2] 772.48/297.04 = [0()] 772.48/297.04 772.48/297.04 772.48/297.04 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 772.48/297.04 772.48/297.04 We are left with following problem, upon which TcT provides the 772.48/297.04 certificate MAYBE. 772.48/297.04 772.48/297.04 Strict Trs: 772.48/297.04 { minus(x, x) -> 0() 772.48/297.04 , le(0(), y) -> true() 772.48/297.04 , le(s(x), 0()) -> false() 772.48/297.04 , le(s(x), s(y)) -> le(x, y) } 772.48/297.04 Weak Trs: 772.48/297.04 { minus(x, 0()) -> x 772.48/297.04 , minus(0(), x) -> 0() 772.48/297.04 , minus(s(x), s(y)) -> minus(x, y) 772.48/297.04 , quot(x, y) -> if_quot(minus(x, y), y, le(y, 0()), le(y, x)) 772.48/297.04 , if_quot(x, y, true(), z) -> divByZeroError() 772.48/297.04 , if_quot(x, y, false(), true()) -> s(quot(x, y)) 772.48/297.04 , if_quot(x, y, false(), false()) -> 0() } 772.48/297.04 Obligation: 772.48/297.04 innermost runtime complexity 772.48/297.04 Answer: 772.48/297.04 MAYBE 772.48/297.04 772.48/297.04 The weightgap principle applies (using the following nonconstant 772.48/297.04 growth matrix-interpretation) 772.48/297.04 772.48/297.04 The following argument positions are usable: 772.48/297.04 Uargs(s) = {1}, Uargs(if_quot) = {1, 3, 4} 772.48/297.04 772.48/297.04 TcT has computed the following matrix interpretation satisfying 772.48/297.04 not(EDA) and not(IDA(1)). 772.48/297.04 772.48/297.04 [minus](x1, x2) = [1] x1 + [2] 772.48/297.04 772.48/297.04 [0] = [1] 772.48/297.04 772.48/297.04 [s](x1) = [1] x1 + [1] 772.48/297.04 772.48/297.04 [le](x1, x2) = [0] 772.48/297.04 772.48/297.04 [true] = [4] 772.48/297.04 772.48/297.04 [false] = [4] 772.48/297.04 772.48/297.04 [quot](x1, x2) = [1] x1 + [5] 772.48/297.04 772.48/297.04 [if_quot](x1, x2, x3, x4) = [1] x1 + [1] x3 + [1] x4 + [1] 772.48/297.04 772.48/297.04 [divByZeroError] = [5] 772.48/297.04 772.48/297.04 The order satisfies the following ordering constraints: 772.48/297.04 772.48/297.04 [minus(x, x)] = [1] x + [2] 772.48/297.04 > [1] 772.48/297.04 = [0()] 772.48/297.04 772.48/297.04 [minus(x, 0())] = [1] x + [2] 772.48/297.04 > [1] x + [0] 772.48/297.04 = [x] 772.48/297.04 772.48/297.04 [minus(0(), x)] = [3] 772.48/297.04 > [1] 772.48/297.04 = [0()] 772.48/297.04 772.48/297.04 [minus(s(x), s(y))] = [1] x + [3] 772.48/297.04 > [1] x + [2] 772.48/297.04 = [minus(x, y)] 772.48/297.04 772.48/297.04 [le(0(), y)] = [0] 772.48/297.04 ? [4] 772.48/297.04 = [true()] 772.48/297.04 772.48/297.04 [le(s(x), 0())] = [0] 772.48/297.04 ? [4] 772.48/297.04 = [false()] 772.48/297.04 772.48/297.04 [le(s(x), s(y))] = [0] 772.48/297.04 >= [0] 772.48/297.04 = [le(x, y)] 772.48/297.04 772.48/297.04 [quot(x, y)] = [1] x + [5] 772.48/297.04 > [1] x + [3] 772.48/297.04 = [if_quot(minus(x, y), y, le(y, 0()), le(y, x))] 772.48/297.04 772.48/297.04 [if_quot(x, y, true(), z)] = [1] x + [1] z + [5] 772.48/297.04 >= [5] 772.48/297.04 = [divByZeroError()] 772.48/297.04 772.48/297.04 [if_quot(x, y, false(), true())] = [1] x + [9] 772.48/297.04 > [1] x + [6] 772.48/297.04 = [s(quot(x, y))] 772.48/297.04 772.48/297.04 [if_quot(x, y, false(), false())] = [1] x + [9] 772.48/297.04 > [1] 772.48/297.04 = [0()] 772.48/297.04 772.48/297.04 772.48/297.04 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 772.48/297.04 772.48/297.04 We are left with following problem, upon which TcT provides the 772.48/297.04 certificate MAYBE. 772.48/297.04 772.48/297.04 Strict Trs: 772.48/297.04 { le(0(), y) -> true() 772.48/297.04 , le(s(x), 0()) -> false() 772.48/297.04 , le(s(x), s(y)) -> le(x, y) } 772.48/297.04 Weak Trs: 772.48/297.04 { minus(x, x) -> 0() 772.48/297.04 , minus(x, 0()) -> x 772.48/297.04 , minus(0(), x) -> 0() 772.48/297.04 , minus(s(x), s(y)) -> minus(x, y) 772.48/297.04 , quot(x, y) -> if_quot(minus(x, y), y, le(y, 0()), le(y, x)) 772.48/297.04 , if_quot(x, y, true(), z) -> divByZeroError() 772.48/297.04 , if_quot(x, y, false(), true()) -> s(quot(x, y)) 772.48/297.04 , if_quot(x, y, false(), false()) -> 0() } 772.48/297.04 Obligation: 772.48/297.04 innermost runtime complexity 772.48/297.04 Answer: 772.48/297.04 MAYBE 772.48/297.04 772.48/297.04 The weightgap principle applies (using the following nonconstant 772.48/297.04 growth matrix-interpretation) 772.48/297.04 772.48/297.04 The following argument positions are usable: 772.48/297.04 Uargs(s) = {1}, Uargs(if_quot) = {1, 3, 4} 772.48/297.04 772.48/297.04 TcT has computed the following matrix interpretation satisfying 772.48/297.04 not(EDA) and not(IDA(1)). 772.48/297.04 772.48/297.04 [minus](x1, x2) = [1] x1 + [0] 772.48/297.04 772.48/297.04 [0] = [0] 772.48/297.04 772.48/297.04 [s](x1) = [1] x1 + [1] 772.48/297.04 772.48/297.04 [le](x1, x2) = [2] 772.48/297.04 772.48/297.04 [true] = [7] 772.48/297.04 772.48/297.04 [false] = [1] 772.48/297.04 772.48/297.04 [quot](x1, x2) = [1] x1 + [5] 772.48/297.04 772.48/297.04 [if_quot](x1, x2, x3, x4) = [1] x1 + [1] x3 + [1] x4 + [1] 772.48/297.04 772.48/297.04 [divByZeroError] = [0] 772.48/297.04 772.48/297.04 The order satisfies the following ordering constraints: 772.48/297.04 772.48/297.04 [minus(x, x)] = [1] x + [0] 772.48/297.04 >= [0] 772.48/297.04 = [0()] 772.48/297.04 772.48/297.04 [minus(x, 0())] = [1] x + [0] 772.48/297.04 >= [1] x + [0] 772.48/297.04 = [x] 772.48/297.04 772.48/297.04 [minus(0(), x)] = [0] 772.48/297.04 >= [0] 772.48/297.04 = [0()] 772.48/297.04 772.48/297.04 [minus(s(x), s(y))] = [1] x + [1] 772.48/297.04 > [1] x + [0] 772.48/297.04 = [minus(x, y)] 772.48/297.04 772.48/297.04 [le(0(), y)] = [2] 772.48/297.04 ? [7] 772.48/297.04 = [true()] 772.48/297.04 772.48/297.04 [le(s(x), 0())] = [2] 772.48/297.04 > [1] 772.48/297.04 = [false()] 772.48/297.04 772.48/297.04 [le(s(x), s(y))] = [2] 772.48/297.04 >= [2] 772.48/297.04 = [le(x, y)] 772.48/297.04 772.48/297.04 [quot(x, y)] = [1] x + [5] 772.48/297.04 >= [1] x + [5] 772.48/297.04 = [if_quot(minus(x, y), y, le(y, 0()), le(y, x))] 772.48/297.04 772.48/297.04 [if_quot(x, y, true(), z)] = [1] x + [1] z + [8] 772.48/297.04 > [0] 772.48/297.04 = [divByZeroError()] 772.48/297.04 772.48/297.04 [if_quot(x, y, false(), true())] = [1] x + [9] 772.48/297.04 > [1] x + [6] 772.48/297.04 = [s(quot(x, y))] 772.48/297.04 772.48/297.04 [if_quot(x, y, false(), false())] = [1] x + [3] 772.48/297.04 > [0] 772.48/297.04 = [0()] 772.48/297.04 772.48/297.04 772.48/297.04 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 772.48/297.04 772.48/297.04 We are left with following problem, upon which TcT provides the 772.48/297.04 certificate MAYBE. 772.48/297.04 772.48/297.04 Strict Trs: 772.48/297.04 { le(0(), y) -> true() 772.48/297.04 , le(s(x), s(y)) -> le(x, y) } 772.48/297.04 Weak Trs: 772.48/297.04 { minus(x, x) -> 0() 772.48/297.04 , minus(x, 0()) -> x 772.48/297.04 , minus(0(), x) -> 0() 772.48/297.04 , minus(s(x), s(y)) -> minus(x, y) 772.48/297.04 , le(s(x), 0()) -> false() 772.48/297.04 , quot(x, y) -> if_quot(minus(x, y), y, le(y, 0()), le(y, x)) 772.48/297.04 , if_quot(x, y, true(), z) -> divByZeroError() 772.48/297.04 , if_quot(x, y, false(), true()) -> s(quot(x, y)) 772.48/297.04 , if_quot(x, y, false(), false()) -> 0() } 772.48/297.04 Obligation: 772.48/297.04 innermost runtime complexity 772.48/297.04 Answer: 772.48/297.04 MAYBE 772.48/297.04 772.48/297.04 None of the processors succeeded. 772.48/297.04 772.48/297.04 Details of failed attempt(s): 772.48/297.04 ----------------------------- 772.48/297.04 1) 'empty' failed due to the following reason: 772.48/297.04 772.48/297.04 Empty strict component of the problem is NOT empty. 772.48/297.04 772.48/297.04 2) 'With Problem ...' failed due to the following reason: 772.48/297.04 772.48/297.04 None of the processors succeeded. 772.48/297.04 772.48/297.04 Details of failed attempt(s): 772.48/297.04 ----------------------------- 772.48/297.04 1) 'empty' failed due to the following reason: 772.48/297.04 772.48/297.04 Empty strict component of the problem is NOT empty. 772.48/297.04 772.48/297.04 2) 'Fastest' failed due to the following reason: 772.48/297.04 772.48/297.04 None of the processors succeeded. 772.48/297.04 772.48/297.04 Details of failed attempt(s): 772.48/297.04 ----------------------------- 772.48/297.04 1) 'With Problem ...' failed due to the following reason: 772.48/297.04 772.48/297.04 None of the processors succeeded. 772.48/297.04 772.48/297.04 Details of failed attempt(s): 772.48/297.04 ----------------------------- 772.48/297.04 1) 'empty' failed due to the following reason: 772.48/297.04 772.48/297.04 Empty strict component of the problem is NOT empty. 772.48/297.04 772.48/297.04 2) 'With Problem ...' failed due to the following reason: 772.48/297.04 772.48/297.04 Empty strict component of the problem is NOT empty. 772.48/297.04 772.48/297.04 772.48/297.04 2) 'With Problem ...' failed due to the following reason: 772.48/297.04 772.48/297.04 None of the processors succeeded. 772.48/297.04 772.48/297.04 Details of failed attempt(s): 772.48/297.04 ----------------------------- 772.48/297.04 1) 'empty' failed due to the following reason: 772.48/297.04 772.48/297.04 Empty strict component of the problem is NOT empty. 772.48/297.04 772.48/297.04 2) 'With Problem ...' failed due to the following reason: 772.48/297.04 772.48/297.04 None of the processors succeeded. 772.48/297.04 772.48/297.04 Details of failed attempt(s): 772.48/297.04 ----------------------------- 772.48/297.04 1) 'empty' failed due to the following reason: 772.48/297.04 772.48/297.04 Empty strict component of the problem is NOT empty. 772.48/297.04 772.48/297.04 2) 'With Problem ...' failed due to the following reason: 772.48/297.04 772.48/297.04 None of the processors succeeded. 772.48/297.04 772.48/297.04 Details of failed attempt(s): 772.48/297.04 ----------------------------- 772.48/297.04 1) 'empty' failed due to the following reason: 772.48/297.04 772.48/297.04 Empty strict component of the problem is NOT empty. 772.48/297.04 772.48/297.04 2) 'With Problem ...' failed due to the following reason: 772.48/297.04 772.48/297.04 Empty strict component of the problem is NOT empty. 772.48/297.04 772.48/297.04 772.48/297.04 772.48/297.04 772.48/297.04 772.48/297.04 772.48/297.04 772.48/297.04 2) 'Best' failed due to the following reason: 772.48/297.04 772.48/297.04 None of the processors succeeded. 772.48/297.04 772.48/297.04 Details of failed attempt(s): 772.48/297.04 ----------------------------- 772.48/297.04 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 772.48/297.04 following reason: 772.48/297.04 772.48/297.04 The input cannot be shown compatible 772.48/297.04 772.48/297.04 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 772.48/297.04 to the following reason: 772.48/297.04 772.48/297.04 The input cannot be shown compatible 772.48/297.04 772.48/297.04 772.48/297.04 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 772.48/297.04 failed due to the following reason: 772.48/297.04 772.48/297.04 None of the processors succeeded. 772.48/297.04 772.48/297.04 Details of failed attempt(s): 772.48/297.04 ----------------------------- 772.48/297.04 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 772.48/297.04 failed due to the following reason: 772.48/297.04 772.48/297.04 match-boundness of the problem could not be verified. 772.48/297.04 772.48/297.04 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 772.48/297.04 failed due to the following reason: 772.48/297.04 772.48/297.04 match-boundness of the problem could not be verified. 772.48/297.04 772.48/297.04 772.48/297.04 772.48/297.04 772.48/297.04 772.48/297.04 Arrrr.. 772.82/297.31 EOF