MAYBE 711.95/297.02 MAYBE 711.95/297.02 711.95/297.02 We are left with following problem, upon which TcT provides the 711.95/297.02 certificate MAYBE. 711.95/297.02 711.95/297.02 Strict Trs: 711.95/297.02 { le(0(), y) -> true() 711.95/297.02 , le(s(x), 0()) -> false() 711.95/297.02 , le(s(x), s(y)) -> le(x, y) 711.95/297.02 , minus(x, 0()) -> x 711.95/297.02 , minus(0(), s(y)) -> 0() 711.95/297.02 , minus(s(x), s(y)) -> minus(x, y) 711.95/297.02 , plus(x, 0()) -> x 711.95/297.02 , plus(x, s(y)) -> s(plus(x, y)) 711.95/297.02 , mod(x, s(y)) -> help(x, s(y), 0()) 711.95/297.02 , mod(s(x), 0()) -> 0() 711.95/297.02 , help(x, s(y), c) -> if(le(c, x), x, s(y), c) 711.95/297.02 , if(true(), x, s(y), c) -> help(x, s(y), plus(c, s(y))) 711.95/297.02 , if(false(), x, s(y), c) -> minus(x, minus(c, s(y))) } 711.95/297.02 Obligation: 711.95/297.02 innermost runtime complexity 711.95/297.02 Answer: 711.95/297.02 MAYBE 711.95/297.02 711.95/297.02 None of the processors succeeded. 711.95/297.02 711.95/297.02 Details of failed attempt(s): 711.95/297.02 ----------------------------- 711.95/297.02 1) 'empty' failed due to the following reason: 711.95/297.02 711.95/297.02 Empty strict component of the problem is NOT empty. 711.95/297.02 711.95/297.02 2) 'Best' failed due to the following reason: 711.95/297.02 711.95/297.02 None of the processors succeeded. 711.95/297.02 711.95/297.02 Details of failed attempt(s): 711.95/297.02 ----------------------------- 711.95/297.02 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 711.95/297.02 following reason: 711.95/297.02 711.95/297.02 Computation stopped due to timeout after 297.0 seconds. 711.95/297.02 711.95/297.02 2) 'Best' failed due to the following reason: 711.95/297.02 711.95/297.02 None of the processors succeeded. 711.95/297.02 711.95/297.02 Details of failed attempt(s): 711.95/297.02 ----------------------------- 711.95/297.02 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 711.95/297.02 seconds)' failed due to the following reason: 711.95/297.02 711.95/297.02 The weightgap principle applies (using the following nonconstant 711.95/297.02 growth matrix-interpretation) 711.95/297.02 711.95/297.02 The following argument positions are usable: 711.95/297.02 Uargs(s) = {1}, Uargs(minus) = {2}, Uargs(help) = {3}, 711.95/297.02 Uargs(if) = {1} 711.95/297.02 711.95/297.02 TcT has computed the following matrix interpretation satisfying 711.95/297.02 not(EDA) and not(IDA(1)). 711.95/297.02 711.95/297.02 [le](x1, x2) = [0] 711.95/297.02 711.95/297.02 [0] = [0] 711.95/297.02 711.95/297.02 [true] = [0] 711.95/297.02 711.95/297.02 [s](x1) = [1] x1 + [0] 711.95/297.02 711.95/297.02 [false] = [0] 711.95/297.02 711.95/297.02 [minus](x1, x2) = [1] x1 + [1] x2 + [0] 711.95/297.02 711.95/297.02 [plus](x1, x2) = [1] x1 + [1] 711.95/297.02 711.95/297.02 [mod](x1, x2) = [1] x1 + [1] x2 + [0] 711.95/297.02 711.95/297.02 [help](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 711.95/297.02 711.95/297.02 [if](x1, x2, x3, x4) = [1] x1 + [1] x2 + [1] x3 + [1] x4 + [0] 711.95/297.02 711.95/297.02 The order satisfies the following ordering constraints: 711.95/297.02 711.95/297.02 [le(0(), y)] = [0] 711.95/297.02 >= [0] 711.95/297.02 = [true()] 711.95/297.02 711.95/297.02 [le(s(x), 0())] = [0] 711.95/297.02 >= [0] 711.95/297.02 = [false()] 711.95/297.02 711.95/297.02 [le(s(x), s(y))] = [0] 711.95/297.02 >= [0] 711.95/297.02 = [le(x, y)] 711.95/297.02 711.95/297.02 [minus(x, 0())] = [1] x + [0] 711.95/297.02 >= [1] x + [0] 711.95/297.02 = [x] 711.95/297.02 711.95/297.02 [minus(0(), s(y))] = [1] y + [0] 711.95/297.02 >= [0] 711.95/297.02 = [0()] 711.95/297.02 711.95/297.02 [minus(s(x), s(y))] = [1] y + [1] x + [0] 711.95/297.02 >= [1] y + [1] x + [0] 711.95/297.02 = [minus(x, y)] 711.95/297.02 711.95/297.02 [plus(x, 0())] = [1] x + [1] 711.95/297.02 > [1] x + [0] 711.95/297.02 = [x] 711.95/297.02 711.95/297.02 [plus(x, s(y))] = [1] x + [1] 711.95/297.02 >= [1] x + [1] 711.95/297.02 = [s(plus(x, y))] 711.95/297.02 711.95/297.02 [mod(x, s(y))] = [1] y + [1] x + [0] 711.95/297.02 >= [1] y + [1] x + [0] 711.95/297.02 = [help(x, s(y), 0())] 711.95/297.02 711.95/297.02 [mod(s(x), 0())] = [1] x + [0] 711.95/297.02 >= [0] 711.95/297.02 = [0()] 711.95/297.02 711.95/297.02 [help(x, s(y), c)] = [1] y + [1] x + [1] c + [0] 711.95/297.02 >= [1] y + [1] x + [1] c + [0] 711.95/297.02 = [if(le(c, x), x, s(y), c)] 711.95/297.02 711.95/297.02 [if(true(), x, s(y), c)] = [1] y + [1] x + [1] c + [0] 711.95/297.02 ? [1] y + [1] x + [1] c + [1] 711.95/297.02 = [help(x, s(y), plus(c, s(y)))] 711.95/297.02 711.95/297.02 [if(false(), x, s(y), c)] = [1] y + [1] x + [1] c + [0] 711.95/297.02 >= [1] y + [1] x + [1] c + [0] 711.95/297.02 = [minus(x, minus(c, s(y)))] 711.95/297.02 711.95/297.02 711.95/297.02 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 711.95/297.02 711.95/297.02 We are left with following problem, upon which TcT provides the 711.95/297.02 certificate MAYBE. 711.95/297.02 711.95/297.02 Strict Trs: 711.95/297.02 { le(0(), y) -> true() 711.95/297.02 , le(s(x), 0()) -> false() 711.95/297.02 , le(s(x), s(y)) -> le(x, y) 711.95/297.02 , minus(x, 0()) -> x 711.95/297.02 , minus(0(), s(y)) -> 0() 711.95/297.02 , minus(s(x), s(y)) -> minus(x, y) 711.95/297.02 , plus(x, s(y)) -> s(plus(x, y)) 711.95/297.02 , mod(x, s(y)) -> help(x, s(y), 0()) 711.95/297.02 , mod(s(x), 0()) -> 0() 711.95/297.02 , help(x, s(y), c) -> if(le(c, x), x, s(y), c) 711.95/297.02 , if(true(), x, s(y), c) -> help(x, s(y), plus(c, s(y))) 711.95/297.02 , if(false(), x, s(y), c) -> minus(x, minus(c, s(y))) } 711.95/297.02 Weak Trs: { plus(x, 0()) -> x } 711.95/297.02 Obligation: 711.95/297.02 innermost runtime complexity 711.95/297.02 Answer: 711.95/297.02 MAYBE 711.95/297.02 711.95/297.02 The weightgap principle applies (using the following nonconstant 711.95/297.02 growth matrix-interpretation) 711.95/297.02 711.95/297.02 The following argument positions are usable: 711.95/297.02 Uargs(s) = {1}, Uargs(minus) = {2}, Uargs(help) = {3}, 711.95/297.02 Uargs(if) = {1} 711.95/297.02 711.95/297.02 TcT has computed the following matrix interpretation satisfying 711.95/297.02 not(EDA) and not(IDA(1)). 711.95/297.02 711.95/297.02 [le](x1, x2) = [4] 711.95/297.02 711.95/297.02 [0] = [0] 711.95/297.02 711.95/297.02 [true] = [0] 711.95/297.02 711.95/297.02 [s](x1) = [1] x1 + [0] 711.95/297.02 711.95/297.02 [false] = [0] 711.95/297.02 711.95/297.02 [minus](x1, x2) = [1] x1 + [1] x2 + [0] 711.95/297.02 711.95/297.02 [plus](x1, x2) = [1] x1 + [0] 711.95/297.02 711.95/297.02 [mod](x1, x2) = [1] x1 + [1] x2 + [0] 711.95/297.02 711.95/297.02 [help](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 711.95/297.02 711.95/297.02 [if](x1, x2, x3, x4) = [1] x1 + [1] x2 + [1] x3 + [1] x4 + [0] 711.95/297.02 711.95/297.02 The order satisfies the following ordering constraints: 711.95/297.02 711.95/297.02 [le(0(), y)] = [4] 711.95/297.02 > [0] 711.95/297.02 = [true()] 711.95/297.02 711.95/297.02 [le(s(x), 0())] = [4] 711.95/297.02 > [0] 711.95/297.02 = [false()] 711.95/297.02 711.95/297.02 [le(s(x), s(y))] = [4] 711.95/297.02 >= [4] 711.95/297.02 = [le(x, y)] 711.95/297.02 711.95/297.02 [minus(x, 0())] = [1] x + [0] 711.95/297.02 >= [1] x + [0] 711.95/297.02 = [x] 711.95/297.02 711.95/297.02 [minus(0(), s(y))] = [1] y + [0] 711.95/297.02 >= [0] 711.95/297.02 = [0()] 711.95/297.02 711.95/297.02 [minus(s(x), s(y))] = [1] y + [1] x + [0] 711.95/297.02 >= [1] y + [1] x + [0] 711.95/297.02 = [minus(x, y)] 711.95/297.02 711.95/297.02 [plus(x, 0())] = [1] x + [0] 711.95/297.02 >= [1] x + [0] 711.95/297.02 = [x] 711.95/297.02 711.95/297.02 [plus(x, s(y))] = [1] x + [0] 711.95/297.02 >= [1] x + [0] 711.95/297.02 = [s(plus(x, y))] 711.95/297.02 711.95/297.02 [mod(x, s(y))] = [1] y + [1] x + [0] 711.95/297.02 >= [1] y + [1] x + [0] 711.95/297.02 = [help(x, s(y), 0())] 711.95/297.02 711.95/297.02 [mod(s(x), 0())] = [1] x + [0] 711.95/297.02 >= [0] 711.95/297.02 = [0()] 711.95/297.02 711.95/297.02 [help(x, s(y), c)] = [1] y + [1] x + [1] c + [0] 711.95/297.02 ? [1] y + [1] x + [1] c + [4] 711.95/297.02 = [if(le(c, x), x, s(y), c)] 711.95/297.02 711.95/297.02 [if(true(), x, s(y), c)] = [1] y + [1] x + [1] c + [0] 711.95/297.02 >= [1] y + [1] x + [1] c + [0] 711.95/297.02 = [help(x, s(y), plus(c, s(y)))] 711.95/297.02 711.95/297.02 [if(false(), x, s(y), c)] = [1] y + [1] x + [1] c + [0] 711.95/297.02 >= [1] y + [1] x + [1] c + [0] 711.95/297.02 = [minus(x, minus(c, s(y)))] 711.95/297.02 711.95/297.02 711.95/297.02 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 711.95/297.02 711.95/297.02 We are left with following problem, upon which TcT provides the 711.95/297.02 certificate MAYBE. 711.95/297.02 711.95/297.02 Strict Trs: 711.95/297.02 { le(s(x), s(y)) -> le(x, y) 711.95/297.02 , minus(x, 0()) -> x 711.95/297.02 , minus(0(), s(y)) -> 0() 711.95/297.02 , minus(s(x), s(y)) -> minus(x, y) 711.95/297.02 , plus(x, s(y)) -> s(plus(x, y)) 711.95/297.02 , mod(x, s(y)) -> help(x, s(y), 0()) 711.95/297.02 , mod(s(x), 0()) -> 0() 711.95/297.02 , help(x, s(y), c) -> if(le(c, x), x, s(y), c) 711.95/297.02 , if(true(), x, s(y), c) -> help(x, s(y), plus(c, s(y))) 711.95/297.02 , if(false(), x, s(y), c) -> minus(x, minus(c, s(y))) } 711.95/297.03 Weak Trs: 711.95/297.03 { le(0(), y) -> true() 711.95/297.03 , le(s(x), 0()) -> false() 711.95/297.03 , plus(x, 0()) -> x } 711.95/297.03 Obligation: 711.95/297.03 innermost runtime complexity 711.95/297.03 Answer: 711.95/297.03 MAYBE 711.95/297.03 711.95/297.03 The weightgap principle applies (using the following nonconstant 711.95/297.03 growth matrix-interpretation) 711.95/297.03 711.95/297.03 The following argument positions are usable: 711.95/297.03 Uargs(s) = {1}, Uargs(minus) = {2}, Uargs(help) = {3}, 711.95/297.03 Uargs(if) = {1} 711.95/297.03 711.95/297.03 TcT has computed the following matrix interpretation satisfying 711.95/297.03 not(EDA) and not(IDA(1)). 711.95/297.03 711.95/297.03 [le](x1, x2) = [4] 711.95/297.03 711.95/297.03 [0] = [0] 711.95/297.03 711.95/297.03 [true] = [0] 711.95/297.03 711.95/297.03 [s](x1) = [1] x1 + [0] 711.95/297.03 711.95/297.03 [false] = [0] 711.95/297.03 711.95/297.03 [minus](x1, x2) = [1] x1 + [1] x2 + [4] 711.95/297.03 711.95/297.03 [plus](x1, x2) = [1] x1 + [0] 711.95/297.03 711.95/297.03 [mod](x1, x2) = [1] x1 + [1] x2 + [0] 711.95/297.03 711.95/297.03 [help](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 711.95/297.03 711.95/297.03 [if](x1, x2, x3, x4) = [1] x1 + [1] x2 + [1] x3 + [1] x4 + [0] 711.95/297.03 711.95/297.03 The order satisfies the following ordering constraints: 711.95/297.03 711.95/297.03 [le(0(), y)] = [4] 711.95/297.03 > [0] 711.95/297.03 = [true()] 711.95/297.03 711.95/297.03 [le(s(x), 0())] = [4] 711.95/297.03 > [0] 711.95/297.03 = [false()] 711.95/297.03 711.95/297.03 [le(s(x), s(y))] = [4] 711.95/297.03 >= [4] 711.95/297.03 = [le(x, y)] 711.95/297.03 711.95/297.03 [minus(x, 0())] = [1] x + [4] 711.95/297.03 > [1] x + [0] 711.95/297.03 = [x] 711.95/297.03 711.95/297.03 [minus(0(), s(y))] = [1] y + [4] 711.95/297.03 > [0] 711.95/297.03 = [0()] 711.95/297.03 711.95/297.03 [minus(s(x), s(y))] = [1] y + [1] x + [4] 711.95/297.03 >= [1] y + [1] x + [4] 711.95/297.03 = [minus(x, y)] 711.95/297.03 711.95/297.03 [plus(x, 0())] = [1] x + [0] 711.95/297.03 >= [1] x + [0] 711.95/297.03 = [x] 711.95/297.03 711.95/297.03 [plus(x, s(y))] = [1] x + [0] 711.95/297.03 >= [1] x + [0] 711.95/297.03 = [s(plus(x, y))] 711.95/297.03 711.95/297.03 [mod(x, s(y))] = [1] y + [1] x + [0] 711.95/297.03 >= [1] y + [1] x + [0] 711.95/297.03 = [help(x, s(y), 0())] 711.95/297.03 711.95/297.03 [mod(s(x), 0())] = [1] x + [0] 711.95/297.03 >= [0] 711.95/297.03 = [0()] 711.95/297.03 711.95/297.03 [help(x, s(y), c)] = [1] y + [1] x + [1] c + [0] 711.95/297.03 ? [1] y + [1] x + [1] c + [4] 711.95/297.03 = [if(le(c, x), x, s(y), c)] 711.95/297.03 711.95/297.03 [if(true(), x, s(y), c)] = [1] y + [1] x + [1] c + [0] 711.95/297.03 >= [1] y + [1] x + [1] c + [0] 711.95/297.03 = [help(x, s(y), plus(c, s(y)))] 711.95/297.03 711.95/297.03 [if(false(), x, s(y), c)] = [1] y + [1] x + [1] c + [0] 711.95/297.03 ? [1] y + [1] x + [1] c + [8] 711.95/297.03 = [minus(x, minus(c, s(y)))] 711.95/297.03 711.95/297.03 711.95/297.03 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 711.95/297.03 711.95/297.03 We are left with following problem, upon which TcT provides the 711.95/297.03 certificate MAYBE. 711.95/297.03 711.95/297.03 Strict Trs: 711.95/297.03 { le(s(x), s(y)) -> le(x, y) 711.95/297.03 , minus(s(x), s(y)) -> minus(x, y) 711.95/297.03 , plus(x, s(y)) -> s(plus(x, y)) 711.95/297.03 , mod(x, s(y)) -> help(x, s(y), 0()) 711.95/297.03 , mod(s(x), 0()) -> 0() 711.95/297.03 , help(x, s(y), c) -> if(le(c, x), x, s(y), c) 711.95/297.03 , if(true(), x, s(y), c) -> help(x, s(y), plus(c, s(y))) 711.95/297.03 , if(false(), x, s(y), c) -> minus(x, minus(c, s(y))) } 711.95/297.03 Weak Trs: 711.95/297.03 { le(0(), y) -> true() 711.95/297.03 , le(s(x), 0()) -> false() 711.95/297.03 , minus(x, 0()) -> x 711.95/297.03 , minus(0(), s(y)) -> 0() 711.95/297.03 , plus(x, 0()) -> x } 711.95/297.03 Obligation: 711.95/297.03 innermost runtime complexity 711.95/297.03 Answer: 711.95/297.03 MAYBE 711.95/297.03 711.95/297.03 The weightgap principle applies (using the following nonconstant 711.95/297.03 growth matrix-interpretation) 711.95/297.03 711.95/297.03 The following argument positions are usable: 711.95/297.03 Uargs(s) = {1}, Uargs(minus) = {2}, Uargs(help) = {3}, 711.95/297.03 Uargs(if) = {1} 711.95/297.03 711.95/297.03 TcT has computed the following matrix interpretation satisfying 711.95/297.03 not(EDA) and not(IDA(1)). 711.95/297.03 711.95/297.03 [le](x1, x2) = [0] 711.95/297.03 711.95/297.03 [0] = [0] 711.95/297.03 711.95/297.03 [true] = [0] 711.95/297.03 711.95/297.03 [s](x1) = [1] x1 + [0] 711.95/297.03 711.95/297.03 [false] = [0] 711.95/297.03 711.95/297.03 [minus](x1, x2) = [1] x1 + [1] x2 + [4] 711.95/297.03 711.95/297.03 [plus](x1, x2) = [1] x1 + [0] 711.95/297.03 711.95/297.03 [mod](x1, x2) = [1] x1 + [1] x2 + [4] 711.95/297.03 711.95/297.03 [help](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 711.95/297.03 711.95/297.03 [if](x1, x2, x3, x4) = [1] x1 + [1] x2 + [1] x3 + [1] x4 + [0] 711.95/297.03 711.95/297.03 The order satisfies the following ordering constraints: 711.95/297.03 711.95/297.03 [le(0(), y)] = [0] 711.95/297.03 >= [0] 711.95/297.03 = [true()] 711.95/297.03 711.95/297.03 [le(s(x), 0())] = [0] 711.95/297.03 >= [0] 711.95/297.03 = [false()] 711.95/297.03 711.95/297.03 [le(s(x), s(y))] = [0] 711.95/297.03 >= [0] 711.95/297.03 = [le(x, y)] 711.95/297.03 711.95/297.03 [minus(x, 0())] = [1] x + [4] 711.95/297.03 > [1] x + [0] 711.95/297.03 = [x] 711.95/297.03 711.95/297.03 [minus(0(), s(y))] = [1] y + [4] 711.95/297.03 > [0] 711.95/297.03 = [0()] 711.95/297.03 711.95/297.03 [minus(s(x), s(y))] = [1] y + [1] x + [4] 711.95/297.03 >= [1] y + [1] x + [4] 711.95/297.03 = [minus(x, y)] 711.95/297.03 711.95/297.03 [plus(x, 0())] = [1] x + [0] 711.95/297.03 >= [1] x + [0] 711.95/297.03 = [x] 711.95/297.03 711.95/297.03 [plus(x, s(y))] = [1] x + [0] 711.95/297.03 >= [1] x + [0] 711.95/297.03 = [s(plus(x, y))] 711.95/297.03 711.95/297.03 [mod(x, s(y))] = [1] y + [1] x + [4] 711.95/297.03 > [1] y + [1] x + [0] 711.95/297.03 = [help(x, s(y), 0())] 711.95/297.03 711.95/297.03 [mod(s(x), 0())] = [1] x + [4] 711.95/297.03 > [0] 711.95/297.03 = [0()] 711.95/297.03 711.95/297.03 [help(x, s(y), c)] = [1] y + [1] x + [1] c + [0] 711.95/297.03 >= [1] y + [1] x + [1] c + [0] 711.95/297.03 = [if(le(c, x), x, s(y), c)] 711.95/297.03 711.95/297.03 [if(true(), x, s(y), c)] = [1] y + [1] x + [1] c + [0] 711.95/297.03 >= [1] y + [1] x + [1] c + [0] 711.95/297.03 = [help(x, s(y), plus(c, s(y)))] 711.95/297.03 711.95/297.03 [if(false(), x, s(y), c)] = [1] y + [1] x + [1] c + [0] 711.95/297.03 ? [1] y + [1] x + [1] c + [8] 711.95/297.03 = [minus(x, minus(c, s(y)))] 711.95/297.03 711.95/297.03 711.95/297.03 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 711.95/297.03 711.95/297.03 We are left with following problem, upon which TcT provides the 711.95/297.03 certificate MAYBE. 711.95/297.03 711.95/297.03 Strict Trs: 711.95/297.03 { le(s(x), s(y)) -> le(x, y) 711.95/297.03 , minus(s(x), s(y)) -> minus(x, y) 711.95/297.03 , plus(x, s(y)) -> s(plus(x, y)) 711.95/297.03 , help(x, s(y), c) -> if(le(c, x), x, s(y), c) 711.95/297.03 , if(true(), x, s(y), c) -> help(x, s(y), plus(c, s(y))) 711.95/297.03 , if(false(), x, s(y), c) -> minus(x, minus(c, s(y))) } 711.95/297.03 Weak Trs: 711.95/297.03 { le(0(), y) -> true() 711.95/297.03 , le(s(x), 0()) -> false() 711.95/297.03 , minus(x, 0()) -> x 711.95/297.03 , minus(0(), s(y)) -> 0() 711.95/297.03 , plus(x, 0()) -> x 711.95/297.03 , mod(x, s(y)) -> help(x, s(y), 0()) 711.95/297.03 , mod(s(x), 0()) -> 0() } 711.95/297.03 Obligation: 711.95/297.03 innermost runtime complexity 711.95/297.03 Answer: 711.95/297.03 MAYBE 711.95/297.03 711.95/297.03 The weightgap principle applies (using the following nonconstant 711.95/297.03 growth matrix-interpretation) 711.95/297.03 711.95/297.03 The following argument positions are usable: 711.95/297.03 Uargs(s) = {1}, Uargs(minus) = {2}, Uargs(help) = {3}, 711.95/297.03 Uargs(if) = {1} 711.95/297.03 711.95/297.03 TcT has computed the following matrix interpretation satisfying 711.95/297.03 not(EDA) and not(IDA(1)). 711.95/297.03 711.95/297.03 [le](x1, x2) = [1] 711.95/297.03 711.95/297.03 [0] = [0] 711.95/297.03 711.95/297.03 [true] = [1] 711.95/297.03 711.95/297.03 [s](x1) = [1] x1 + [0] 711.95/297.03 711.95/297.03 [false] = [0] 711.95/297.03 711.95/297.03 [minus](x1, x2) = [1] x1 + [1] x2 + [4] 711.95/297.03 711.95/297.03 [plus](x1, x2) = [1] x1 + [0] 711.95/297.03 711.95/297.03 [mod](x1, x2) = [1] x1 + [1] x2 + [0] 711.95/297.03 711.95/297.03 [help](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 711.95/297.03 711.95/297.03 [if](x1, x2, x3, x4) = [1] x1 + [1] x2 + [1] x3 + [1] x4 + [0] 711.95/297.03 711.95/297.03 The order satisfies the following ordering constraints: 711.95/297.03 711.95/297.03 [le(0(), y)] = [1] 711.95/297.03 >= [1] 711.95/297.03 = [true()] 711.95/297.03 711.95/297.03 [le(s(x), 0())] = [1] 711.95/297.03 > [0] 711.95/297.03 = [false()] 711.95/297.03 711.95/297.03 [le(s(x), s(y))] = [1] 711.95/297.03 >= [1] 711.95/297.03 = [le(x, y)] 711.95/297.03 711.95/297.03 [minus(x, 0())] = [1] x + [4] 711.95/297.03 > [1] x + [0] 711.95/297.03 = [x] 711.95/297.03 711.95/297.03 [minus(0(), s(y))] = [1] y + [4] 711.95/297.03 > [0] 711.95/297.03 = [0()] 711.95/297.03 711.95/297.03 [minus(s(x), s(y))] = [1] y + [1] x + [4] 711.95/297.03 >= [1] y + [1] x + [4] 711.95/297.03 = [minus(x, y)] 711.95/297.03 711.95/297.03 [plus(x, 0())] = [1] x + [0] 711.95/297.03 >= [1] x + [0] 711.95/297.03 = [x] 711.95/297.03 711.95/297.03 [plus(x, s(y))] = [1] x + [0] 711.95/297.03 >= [1] x + [0] 711.95/297.03 = [s(plus(x, y))] 711.95/297.03 711.95/297.03 [mod(x, s(y))] = [1] y + [1] x + [0] 711.95/297.03 >= [1] y + [1] x + [0] 711.95/297.03 = [help(x, s(y), 0())] 711.95/297.03 711.95/297.03 [mod(s(x), 0())] = [1] x + [0] 711.95/297.03 >= [0] 711.95/297.03 = [0()] 711.95/297.03 711.95/297.03 [help(x, s(y), c)] = [1] y + [1] x + [1] c + [0] 711.95/297.03 ? [1] y + [1] x + [1] c + [1] 711.95/297.03 = [if(le(c, x), x, s(y), c)] 711.95/297.03 711.95/297.03 [if(true(), x, s(y), c)] = [1] y + [1] x + [1] c + [1] 711.95/297.03 > [1] y + [1] x + [1] c + [0] 711.95/297.03 = [help(x, s(y), plus(c, s(y)))] 711.95/297.03 711.95/297.03 [if(false(), x, s(y), c)] = [1] y + [1] x + [1] c + [0] 711.95/297.03 ? [1] y + [1] x + [1] c + [8] 711.95/297.03 = [minus(x, minus(c, s(y)))] 711.95/297.03 711.95/297.03 711.95/297.03 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 711.95/297.03 711.95/297.03 We are left with following problem, upon which TcT provides the 711.95/297.03 certificate MAYBE. 711.95/297.03 711.95/297.03 Strict Trs: 711.95/297.03 { le(s(x), s(y)) -> le(x, y) 711.95/297.03 , minus(s(x), s(y)) -> minus(x, y) 711.95/297.03 , plus(x, s(y)) -> s(plus(x, y)) 711.95/297.03 , help(x, s(y), c) -> if(le(c, x), x, s(y), c) 711.95/297.03 , if(false(), x, s(y), c) -> minus(x, minus(c, s(y))) } 711.95/297.03 Weak Trs: 711.95/297.03 { le(0(), y) -> true() 711.95/297.03 , le(s(x), 0()) -> false() 711.95/297.03 , minus(x, 0()) -> x 711.95/297.03 , minus(0(), s(y)) -> 0() 711.95/297.03 , plus(x, 0()) -> x 711.95/297.03 , mod(x, s(y)) -> help(x, s(y), 0()) 711.95/297.03 , mod(s(x), 0()) -> 0() 711.95/297.03 , if(true(), x, s(y), c) -> help(x, s(y), plus(c, s(y))) } 711.95/297.03 Obligation: 711.95/297.03 innermost runtime complexity 711.95/297.03 Answer: 711.95/297.03 MAYBE 711.95/297.03 711.95/297.03 The weightgap principle applies (using the following nonconstant 711.95/297.03 growth matrix-interpretation) 711.95/297.03 711.95/297.03 The following argument positions are usable: 711.95/297.03 Uargs(s) = {1}, Uargs(minus) = {2}, Uargs(help) = {3}, 711.95/297.03 Uargs(if) = {1} 711.95/297.03 711.95/297.03 TcT has computed the following matrix interpretation satisfying 711.95/297.03 not(EDA) and not(IDA(1)). 711.95/297.03 711.95/297.03 [le](x1, x2) = [4] 711.95/297.03 711.95/297.03 [0] = [0] 711.95/297.03 711.95/297.03 [true] = [0] 711.95/297.03 711.95/297.03 [s](x1) = [1] x1 + [0] 711.95/297.03 711.95/297.03 [false] = [4] 711.95/297.03 711.95/297.03 [minus](x1, x2) = [1] x1 + [1] x2 + [0] 711.95/297.03 711.95/297.03 [plus](x1, x2) = [1] x1 + [0] 711.95/297.03 711.95/297.03 [mod](x1, x2) = [1] x1 + [1] x2 + [0] 711.95/297.03 711.95/297.03 [help](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 711.95/297.03 711.95/297.03 [if](x1, x2, x3, x4) = [1] x1 + [1] x2 + [1] x3 + [1] x4 + [0] 711.95/297.03 711.95/297.03 The order satisfies the following ordering constraints: 711.95/297.03 711.95/297.03 [le(0(), y)] = [4] 711.95/297.03 > [0] 711.95/297.03 = [true()] 711.95/297.03 711.95/297.03 [le(s(x), 0())] = [4] 711.95/297.03 >= [4] 711.95/297.03 = [false()] 711.95/297.03 711.95/297.03 [le(s(x), s(y))] = [4] 711.95/297.03 >= [4] 711.95/297.03 = [le(x, y)] 711.95/297.03 711.95/297.03 [minus(x, 0())] = [1] x + [0] 711.95/297.03 >= [1] x + [0] 711.95/297.03 = [x] 711.95/297.03 711.95/297.03 [minus(0(), s(y))] = [1] y + [0] 711.95/297.03 >= [0] 711.95/297.03 = [0()] 711.95/297.03 711.95/297.03 [minus(s(x), s(y))] = [1] y + [1] x + [0] 711.95/297.03 >= [1] y + [1] x + [0] 711.95/297.03 = [minus(x, y)] 711.95/297.03 711.95/297.03 [plus(x, 0())] = [1] x + [0] 711.95/297.03 >= [1] x + [0] 711.95/297.03 = [x] 711.95/297.03 711.95/297.03 [plus(x, s(y))] = [1] x + [0] 711.95/297.03 >= [1] x + [0] 711.95/297.03 = [s(plus(x, y))] 711.95/297.03 711.95/297.03 [mod(x, s(y))] = [1] y + [1] x + [0] 711.95/297.03 >= [1] y + [1] x + [0] 711.95/297.03 = [help(x, s(y), 0())] 711.95/297.03 711.95/297.03 [mod(s(x), 0())] = [1] x + [0] 711.95/297.03 >= [0] 711.95/297.03 = [0()] 711.95/297.03 711.95/297.03 [help(x, s(y), c)] = [1] y + [1] x + [1] c + [0] 711.95/297.03 ? [1] y + [1] x + [1] c + [4] 711.95/297.03 = [if(le(c, x), x, s(y), c)] 711.95/297.03 711.95/297.03 [if(true(), x, s(y), c)] = [1] y + [1] x + [1] c + [0] 711.95/297.03 >= [1] y + [1] x + [1] c + [0] 711.95/297.03 = [help(x, s(y), plus(c, s(y)))] 711.95/297.03 711.95/297.03 [if(false(), x, s(y), c)] = [1] y + [1] x + [1] c + [4] 711.95/297.03 > [1] y + [1] x + [1] c + [0] 711.95/297.03 = [minus(x, minus(c, s(y)))] 711.95/297.03 711.95/297.03 711.95/297.03 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 711.95/297.03 711.95/297.03 We are left with following problem, upon which TcT provides the 711.95/297.03 certificate MAYBE. 711.95/297.03 711.95/297.03 Strict Trs: 711.95/297.03 { le(s(x), s(y)) -> le(x, y) 711.95/297.03 , minus(s(x), s(y)) -> minus(x, y) 711.95/297.03 , plus(x, s(y)) -> s(plus(x, y)) 711.95/297.03 , help(x, s(y), c) -> if(le(c, x), x, s(y), c) } 711.95/297.03 Weak Trs: 711.95/297.03 { le(0(), y) -> true() 711.95/297.03 , le(s(x), 0()) -> false() 711.95/297.03 , minus(x, 0()) -> x 711.95/297.03 , minus(0(), s(y)) -> 0() 711.95/297.03 , plus(x, 0()) -> x 711.95/297.03 , mod(x, s(y)) -> help(x, s(y), 0()) 711.95/297.03 , mod(s(x), 0()) -> 0() 711.95/297.03 , if(true(), x, s(y), c) -> help(x, s(y), plus(c, s(y))) 711.95/297.03 , if(false(), x, s(y), c) -> minus(x, minus(c, s(y))) } 711.95/297.03 Obligation: 711.95/297.03 innermost runtime complexity 711.95/297.03 Answer: 711.95/297.03 MAYBE 711.95/297.03 711.95/297.03 The weightgap principle applies (using the following nonconstant 711.95/297.03 growth matrix-interpretation) 711.95/297.03 711.95/297.03 The following argument positions are usable: 711.95/297.03 Uargs(s) = {1}, Uargs(minus) = {2}, Uargs(help) = {3}, 711.95/297.03 Uargs(if) = {1} 711.95/297.03 711.95/297.03 TcT has computed the following matrix interpretation satisfying 711.95/297.03 not(EDA) and not(IDA(1)). 711.95/297.03 711.95/297.03 [le](x1, x2) = [4] 711.95/297.03 711.95/297.03 [0] = [0] 711.95/297.03 711.95/297.03 [true] = [4] 711.95/297.03 711.95/297.03 [s](x1) = [1] x1 + [4] 711.95/297.03 711.95/297.03 [false] = [4] 711.95/297.03 711.95/297.03 [minus](x1, x2) = [1] x1 + [1] x2 + [0] 711.95/297.03 711.95/297.03 [plus](x1, x2) = [1] x1 + [0] 711.95/297.03 711.95/297.03 [mod](x1, x2) = [1] x1 + [1] x2 + [0] 711.95/297.03 711.95/297.03 [help](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 711.95/297.03 711.95/297.03 [if](x1, x2, x3, x4) = [1] x1 + [1] x2 + [1] x3 + [1] x4 + [0] 711.95/297.03 711.95/297.03 The order satisfies the following ordering constraints: 711.95/297.03 711.95/297.03 [le(0(), y)] = [4] 711.95/297.03 >= [4] 711.95/297.03 = [true()] 711.95/297.03 711.95/297.03 [le(s(x), 0())] = [4] 711.95/297.03 >= [4] 711.95/297.03 = [false()] 711.95/297.03 711.95/297.03 [le(s(x), s(y))] = [4] 711.95/297.03 >= [4] 711.95/297.03 = [le(x, y)] 711.95/297.03 711.95/297.03 [minus(x, 0())] = [1] x + [0] 711.95/297.03 >= [1] x + [0] 711.95/297.03 = [x] 711.95/297.03 711.95/297.03 [minus(0(), s(y))] = [1] y + [4] 711.95/297.03 > [0] 711.95/297.03 = [0()] 711.95/297.03 711.95/297.03 [minus(s(x), s(y))] = [1] y + [1] x + [8] 711.95/297.03 > [1] y + [1] x + [0] 711.95/297.03 = [minus(x, y)] 711.95/297.03 711.95/297.03 [plus(x, 0())] = [1] x + [0] 711.95/297.03 >= [1] x + [0] 711.95/297.03 = [x] 711.95/297.03 711.95/297.03 [plus(x, s(y))] = [1] x + [0] 711.95/297.03 ? [1] x + [4] 711.95/297.03 = [s(plus(x, y))] 711.95/297.03 711.95/297.03 [mod(x, s(y))] = [1] y + [1] x + [4] 711.95/297.03 >= [1] y + [1] x + [4] 711.95/297.03 = [help(x, s(y), 0())] 711.95/297.03 711.95/297.03 [mod(s(x), 0())] = [1] x + [4] 711.95/297.03 > [0] 711.95/297.03 = [0()] 711.95/297.03 711.95/297.03 [help(x, s(y), c)] = [1] y + [1] x + [1] c + [4] 711.95/297.03 ? [1] y + [1] x + [1] c + [8] 711.95/297.03 = [if(le(c, x), x, s(y), c)] 711.95/297.03 711.95/297.03 [if(true(), x, s(y), c)] = [1] y + [1] x + [1] c + [8] 711.95/297.03 > [1] y + [1] x + [1] c + [4] 711.95/297.03 = [help(x, s(y), plus(c, s(y)))] 711.95/297.03 711.95/297.03 [if(false(), x, s(y), c)] = [1] y + [1] x + [1] c + [8] 711.95/297.03 > [1] y + [1] x + [1] c + [4] 711.95/297.03 = [minus(x, minus(c, s(y)))] 711.95/297.03 711.95/297.03 711.95/297.03 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 711.95/297.03 711.95/297.03 We are left with following problem, upon which TcT provides the 711.95/297.03 certificate MAYBE. 711.95/297.03 711.95/297.03 Strict Trs: 711.95/297.03 { le(s(x), s(y)) -> le(x, y) 711.95/297.03 , plus(x, s(y)) -> s(plus(x, y)) 711.95/297.03 , help(x, s(y), c) -> if(le(c, x), x, s(y), c) } 711.95/297.03 Weak Trs: 711.95/297.03 { le(0(), y) -> true() 711.95/297.03 , le(s(x), 0()) -> false() 711.95/297.03 , minus(x, 0()) -> x 711.95/297.03 , minus(0(), s(y)) -> 0() 711.95/297.03 , minus(s(x), s(y)) -> minus(x, y) 711.95/297.03 , plus(x, 0()) -> x 711.95/297.03 , mod(x, s(y)) -> help(x, s(y), 0()) 711.95/297.03 , mod(s(x), 0()) -> 0() 711.95/297.03 , if(true(), x, s(y), c) -> help(x, s(y), plus(c, s(y))) 711.95/297.03 , if(false(), x, s(y), c) -> minus(x, minus(c, s(y))) } 711.95/297.03 Obligation: 711.95/297.03 innermost runtime complexity 711.95/297.03 Answer: 711.95/297.03 MAYBE 711.95/297.03 711.95/297.03 None of the processors succeeded. 711.95/297.03 711.95/297.03 Details of failed attempt(s): 711.95/297.03 ----------------------------- 711.95/297.03 1) 'empty' failed due to the following reason: 711.95/297.03 711.95/297.03 Empty strict component of the problem is NOT empty. 711.95/297.03 711.95/297.03 2) 'With Problem ...' failed due to the following reason: 711.95/297.03 711.95/297.03 None of the processors succeeded. 711.95/297.03 711.95/297.03 Details of failed attempt(s): 711.95/297.03 ----------------------------- 711.95/297.03 1) 'empty' failed due to the following reason: 711.95/297.03 711.95/297.03 Empty strict component of the problem is NOT empty. 711.95/297.03 711.95/297.03 2) 'Fastest' failed due to the following reason: 711.95/297.03 711.95/297.03 None of the processors succeeded. 711.95/297.03 711.95/297.03 Details of failed attempt(s): 711.95/297.03 ----------------------------- 711.95/297.03 1) 'With Problem ...' failed due to the following reason: 711.95/297.03 711.95/297.03 None of the processors succeeded. 711.95/297.03 711.95/297.03 Details of failed attempt(s): 711.95/297.03 ----------------------------- 711.95/297.03 1) 'empty' failed due to the following reason: 711.95/297.03 711.95/297.03 Empty strict component of the problem is NOT empty. 711.95/297.03 711.95/297.03 2) 'With Problem ...' failed due to the following reason: 711.95/297.03 711.95/297.03 Empty strict component of the problem is NOT empty. 711.95/297.03 711.95/297.03 711.95/297.03 2) 'With Problem ...' failed due to the following reason: 711.95/297.03 711.95/297.03 None of the processors succeeded. 711.95/297.03 711.95/297.03 Details of failed attempt(s): 711.95/297.03 ----------------------------- 711.95/297.03 1) 'empty' failed due to the following reason: 711.95/297.03 711.95/297.03 Empty strict component of the problem is NOT empty. 711.95/297.03 711.95/297.03 2) 'With Problem ...' failed due to the following reason: 711.95/297.03 711.95/297.03 None of the processors succeeded. 711.95/297.03 711.95/297.03 Details of failed attempt(s): 711.95/297.03 ----------------------------- 711.95/297.03 1) 'empty' failed due to the following reason: 711.95/297.03 711.95/297.03 Empty strict component of the problem is NOT empty. 711.95/297.03 711.95/297.03 2) 'With Problem ...' failed due to the following reason: 711.95/297.03 711.95/297.03 None of the processors succeeded. 711.95/297.03 711.95/297.03 Details of failed attempt(s): 711.95/297.03 ----------------------------- 711.95/297.03 1) 'empty' failed due to the following reason: 711.95/297.03 711.95/297.03 Empty strict component of the problem is NOT empty. 711.95/297.03 711.95/297.03 2) 'With Problem ...' failed due to the following reason: 711.95/297.03 711.95/297.03 Empty strict component of the problem is NOT empty. 711.95/297.03 711.95/297.03 711.95/297.03 711.95/297.03 711.95/297.03 711.95/297.03 711.95/297.03 711.95/297.03 2) 'Best' failed due to the following reason: 711.95/297.03 711.95/297.03 None of the processors succeeded. 711.95/297.03 711.95/297.03 Details of failed attempt(s): 711.95/297.03 ----------------------------- 711.95/297.03 1) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 711.95/297.03 to the following reason: 711.95/297.03 711.95/297.03 The input cannot be shown compatible 711.95/297.03 711.95/297.03 2) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 711.95/297.03 following reason: 711.95/297.03 711.95/297.03 The input cannot be shown compatible 711.95/297.03 711.95/297.03 711.95/297.03 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 711.95/297.03 failed due to the following reason: 711.95/297.03 711.95/297.03 None of the processors succeeded. 711.95/297.03 711.95/297.03 Details of failed attempt(s): 711.95/297.03 ----------------------------- 711.95/297.03 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 711.95/297.03 failed due to the following reason: 711.95/297.03 711.95/297.03 match-boundness of the problem could not be verified. 711.95/297.03 711.95/297.03 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 711.95/297.03 failed due to the following reason: 711.95/297.03 711.95/297.03 match-boundness of the problem could not be verified. 711.95/297.03 711.95/297.03 711.95/297.03 711.95/297.03 711.95/297.03 711.95/297.03 Arrrr.. 712.08/297.16 EOF