MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { cond1(true(), x, y, z) -> cond2(gr(y, z), x, y, z) , cond2(true(), x, y, z) -> cond2(gr(y, z), p(x), p(y), z) , cond2(false(), x, y, z) -> cond1(and(eq(x, y), gr(x, z)), x, y, z) , gr(0(), x) -> false() , gr(s(x), 0()) -> true() , gr(s(x), s(y)) -> gr(x, y) , p(0()) -> 0() , p(s(x)) -> x , and(x, false()) -> false() , and(true(), true()) -> true() , and(false(), x) -> false() , eq(0(), 0()) -> true() , eq(0(), s(x)) -> false() , eq(s(x), 0()) -> false() , eq(s(x), s(y)) -> eq(x, y) } Obligation: runtime complexity Answer: MAYBE None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) '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) '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) '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. 2) 'Innermost Weak Dependency Pairs (timeout of 60 seconds)' failed due to the following reason: We add the following weak dependency pairs: Strict DPs: { cond1^#(true(), x, y, z) -> c_1(cond2^#(gr(y, z), x, y, z)) , cond2^#(true(), x, y, z) -> c_2(cond2^#(gr(y, z), p(x), p(y), z)) , cond2^#(false(), x, y, z) -> c_3(cond1^#(and(eq(x, y), gr(x, z)), x, y, z)) , gr^#(0(), x) -> c_4() , gr^#(s(x), 0()) -> c_5() , gr^#(s(x), s(y)) -> c_6(gr^#(x, y)) , p^#(0()) -> c_7() , p^#(s(x)) -> c_8(x) , and^#(x, false()) -> c_9() , and^#(true(), true()) -> c_10() , and^#(false(), x) -> c_11() , eq^#(0(), 0()) -> c_12() , eq^#(0(), s(x)) -> c_13() , eq^#(s(x), 0()) -> c_14() , eq^#(s(x), s(y)) -> c_15(eq^#(x, y)) } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { cond1^#(true(), x, y, z) -> c_1(cond2^#(gr(y, z), x, y, z)) , cond2^#(true(), x, y, z) -> c_2(cond2^#(gr(y, z), p(x), p(y), z)) , cond2^#(false(), x, y, z) -> c_3(cond1^#(and(eq(x, y), gr(x, z)), x, y, z)) , gr^#(0(), x) -> c_4() , gr^#(s(x), 0()) -> c_5() , gr^#(s(x), s(y)) -> c_6(gr^#(x, y)) , p^#(0()) -> c_7() , p^#(s(x)) -> c_8(x) , and^#(x, false()) -> c_9() , and^#(true(), true()) -> c_10() , and^#(false(), x) -> c_11() , eq^#(0(), 0()) -> c_12() , eq^#(0(), s(x)) -> c_13() , eq^#(s(x), 0()) -> c_14() , eq^#(s(x), s(y)) -> c_15(eq^#(x, y)) } Strict Trs: { cond1(true(), x, y, z) -> cond2(gr(y, z), x, y, z) , cond2(true(), x, y, z) -> cond2(gr(y, z), p(x), p(y), z) , cond2(false(), x, y, z) -> cond1(and(eq(x, y), gr(x, z)), x, y, z) , gr(0(), x) -> false() , gr(s(x), 0()) -> true() , gr(s(x), s(y)) -> gr(x, y) , p(0()) -> 0() , p(s(x)) -> x , and(x, false()) -> false() , and(true(), true()) -> true() , and(false(), x) -> false() , eq(0(), 0()) -> true() , eq(0(), s(x)) -> false() , eq(s(x), 0()) -> false() , eq(s(x), s(y)) -> eq(x, y) } Obligation: runtime complexity Answer: MAYBE We estimate the number of application of {4,5,7,9,10,11,12,13,14} by applications of Pre({4,5,7,9,10,11,12,13,14}) = {6,8,15}. Here rules are labeled as follows: DPs: { 1: cond1^#(true(), x, y, z) -> c_1(cond2^#(gr(y, z), x, y, z)) , 2: cond2^#(true(), x, y, z) -> c_2(cond2^#(gr(y, z), p(x), p(y), z)) , 3: cond2^#(false(), x, y, z) -> c_3(cond1^#(and(eq(x, y), gr(x, z)), x, y, z)) , 4: gr^#(0(), x) -> c_4() , 5: gr^#(s(x), 0()) -> c_5() , 6: gr^#(s(x), s(y)) -> c_6(gr^#(x, y)) , 7: p^#(0()) -> c_7() , 8: p^#(s(x)) -> c_8(x) , 9: and^#(x, false()) -> c_9() , 10: and^#(true(), true()) -> c_10() , 11: and^#(false(), x) -> c_11() , 12: eq^#(0(), 0()) -> c_12() , 13: eq^#(0(), s(x)) -> c_13() , 14: eq^#(s(x), 0()) -> c_14() , 15: eq^#(s(x), s(y)) -> c_15(eq^#(x, y)) } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { cond1^#(true(), x, y, z) -> c_1(cond2^#(gr(y, z), x, y, z)) , cond2^#(true(), x, y, z) -> c_2(cond2^#(gr(y, z), p(x), p(y), z)) , cond2^#(false(), x, y, z) -> c_3(cond1^#(and(eq(x, y), gr(x, z)), x, y, z)) , gr^#(s(x), s(y)) -> c_6(gr^#(x, y)) , p^#(s(x)) -> c_8(x) , eq^#(s(x), s(y)) -> c_15(eq^#(x, y)) } Strict Trs: { cond1(true(), x, y, z) -> cond2(gr(y, z), x, y, z) , cond2(true(), x, y, z) -> cond2(gr(y, z), p(x), p(y), z) , cond2(false(), x, y, z) -> cond1(and(eq(x, y), gr(x, z)), x, y, z) , gr(0(), x) -> false() , gr(s(x), 0()) -> true() , gr(s(x), s(y)) -> gr(x, y) , p(0()) -> 0() , p(s(x)) -> x , and(x, false()) -> false() , and(true(), true()) -> true() , and(false(), x) -> false() , eq(0(), 0()) -> true() , eq(0(), s(x)) -> false() , eq(s(x), 0()) -> false() , eq(s(x), s(y)) -> eq(x, y) } Weak DPs: { gr^#(0(), x) -> c_4() , gr^#(s(x), 0()) -> c_5() , p^#(0()) -> c_7() , and^#(x, false()) -> c_9() , and^#(true(), true()) -> c_10() , and^#(false(), x) -> c_11() , eq^#(0(), 0()) -> c_12() , eq^#(0(), s(x)) -> c_13() , eq^#(s(x), 0()) -> c_14() } Obligation: runtime complexity Answer: MAYBE Empty strict component of the problem is NOT empty. Arrrr..