MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { le(0(), y) -> true() , le(s(x), 0()) -> false() , le(s(x), s(y)) -> le(x, y) , mod(x, 0()) -> modZeroErro() , mod(x, s(y)) -> modIter(x, s(y), 0(), 0()) , modIter(x, s(y), z, u) -> if(le(x, z), x, s(y), z, u) , if(true(), x, y, z, u) -> u , if(false(), x, y, z, u) -> if2(le(y, s(u)), x, y, s(z), s(u)) , if2(true(), x, y, z, u) -> modIter(x, y, z, 0()) , if2(false(), x, y, z, u) -> modIter(x, y, z, u) } Obligation: runtime complexity Answer: MAYBE None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'WithProblem (timeout of 60 seconds)' failed due to the following reason: Computation stopped due to timeout after 60.0 seconds. 2) 'Best' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'WithProblem (timeout of 30 seconds) (timeout of 60 seconds)' failed due to the following reason: Computation stopped due to timeout after 30.0 seconds. 2) 'Fastest (timeout of 5 seconds) (timeout of 60 seconds)' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'Bounds with perSymbol-enrichment and initial automaton 'match'' failed due to the following reason: match-boundness of the problem could not be verified. 2) 'Bounds with minimal-enrichment and initial automaton 'match'' failed due to the following reason: match-boundness of the problem could not be verified. 3) 'Best' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'bsearch-popstar (timeout of 60 seconds)' failed due to the following reason: The processor is inapplicable, reason: Processor only applicable for innermost runtime complexity analysis 2) 'Polynomial Path Order (PS) (timeout of 60 seconds)' failed due to the following reason: The processor is inapplicable, reason: Processor only applicable for innermost runtime complexity analysis 3) 'Innermost Weak Dependency Pairs (timeout of 60 seconds)' failed due to the following reason: We add the following weak dependency pairs: Strict DPs: { le^#(0(), y) -> c_1() , le^#(s(x), 0()) -> c_2() , le^#(s(x), s(y)) -> c_3(le^#(x, y)) , mod^#(x, 0()) -> c_4() , mod^#(x, s(y)) -> c_5(modIter^#(x, s(y), 0(), 0())) , modIter^#(x, s(y), z, u) -> c_6(if^#(le(x, z), x, s(y), z, u)) , if^#(true(), x, y, z, u) -> c_7(u) , if^#(false(), x, y, z, u) -> c_8(if2^#(le(y, s(u)), x, y, s(z), s(u))) , if2^#(true(), x, y, z, u) -> c_9(modIter^#(x, y, z, 0())) , if2^#(false(), x, y, z, u) -> c_10(modIter^#(x, y, z, u)) } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { le^#(0(), y) -> c_1() , le^#(s(x), 0()) -> c_2() , le^#(s(x), s(y)) -> c_3(le^#(x, y)) , mod^#(x, 0()) -> c_4() , mod^#(x, s(y)) -> c_5(modIter^#(x, s(y), 0(), 0())) , modIter^#(x, s(y), z, u) -> c_6(if^#(le(x, z), x, s(y), z, u)) , if^#(true(), x, y, z, u) -> c_7(u) , if^#(false(), x, y, z, u) -> c_8(if2^#(le(y, s(u)), x, y, s(z), s(u))) , if2^#(true(), x, y, z, u) -> c_9(modIter^#(x, y, z, 0())) , if2^#(false(), x, y, z, u) -> c_10(modIter^#(x, y, z, u)) } Strict Trs: { le(0(), y) -> true() , le(s(x), 0()) -> false() , le(s(x), s(y)) -> le(x, y) , mod(x, 0()) -> modZeroErro() , mod(x, s(y)) -> modIter(x, s(y), 0(), 0()) , modIter(x, s(y), z, u) -> if(le(x, z), x, s(y), z, u) , if(true(), x, y, z, u) -> u , if(false(), x, y, z, u) -> if2(le(y, s(u)), x, y, s(z), s(u)) , if2(true(), x, y, z, u) -> modIter(x, y, z, 0()) , if2(false(), x, y, z, u) -> modIter(x, y, z, u) } Obligation: runtime complexity Answer: MAYBE We estimate the number of application of {1,2,4} by applications of Pre({1,2,4}) = {3,7}. Here rules are labeled as follows: DPs: { 1: le^#(0(), y) -> c_1() , 2: le^#(s(x), 0()) -> c_2() , 3: le^#(s(x), s(y)) -> c_3(le^#(x, y)) , 4: mod^#(x, 0()) -> c_4() , 5: mod^#(x, s(y)) -> c_5(modIter^#(x, s(y), 0(), 0())) , 6: modIter^#(x, s(y), z, u) -> c_6(if^#(le(x, z), x, s(y), z, u)) , 7: if^#(true(), x, y, z, u) -> c_7(u) , 8: if^#(false(), x, y, z, u) -> c_8(if2^#(le(y, s(u)), x, y, s(z), s(u))) , 9: if2^#(true(), x, y, z, u) -> c_9(modIter^#(x, y, z, 0())) , 10: if2^#(false(), x, y, z, u) -> c_10(modIter^#(x, y, z, u)) } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { le^#(s(x), s(y)) -> c_3(le^#(x, y)) , mod^#(x, s(y)) -> c_5(modIter^#(x, s(y), 0(), 0())) , modIter^#(x, s(y), z, u) -> c_6(if^#(le(x, z), x, s(y), z, u)) , if^#(true(), x, y, z, u) -> c_7(u) , if^#(false(), x, y, z, u) -> c_8(if2^#(le(y, s(u)), x, y, s(z), s(u))) , if2^#(true(), x, y, z, u) -> c_9(modIter^#(x, y, z, 0())) , if2^#(false(), x, y, z, u) -> c_10(modIter^#(x, y, z, u)) } Strict Trs: { le(0(), y) -> true() , le(s(x), 0()) -> false() , le(s(x), s(y)) -> le(x, y) , mod(x, 0()) -> modZeroErro() , mod(x, s(y)) -> modIter(x, s(y), 0(), 0()) , modIter(x, s(y), z, u) -> if(le(x, z), x, s(y), z, u) , if(true(), x, y, z, u) -> u , if(false(), x, y, z, u) -> if2(le(y, s(u)), x, y, s(z), s(u)) , if2(true(), x, y, z, u) -> modIter(x, y, z, 0()) , if2(false(), x, y, z, u) -> modIter(x, y, z, u) } Weak DPs: { le^#(0(), y) -> c_1() , le^#(s(x), 0()) -> c_2() , mod^#(x, 0()) -> c_4() } Obligation: runtime complexity Answer: MAYBE Empty strict component of the problem is NOT empty. Arrrr..