MAYBE 627.72/297.04 MAYBE 627.72/297.04 627.72/297.04 We are left with following problem, upon which TcT provides the 627.72/297.04 certificate MAYBE. 627.72/297.04 627.72/297.04 Strict Trs: 627.72/297.04 { p(X) -> n__p(X) 627.72/297.04 , p(0()) -> 0() 627.72/297.04 , p(s(X)) -> X 627.72/297.04 , 0() -> n__0() 627.72/297.04 , s(X) -> n__s(X) 627.72/297.04 , leq(0(), Y) -> true() 627.72/297.04 , leq(s(X), 0()) -> false() 627.72/297.04 , leq(s(X), s(Y)) -> leq(X, Y) 627.72/297.04 , if(true(), X, Y) -> activate(X) 627.72/297.04 , if(false(), X, Y) -> activate(Y) 627.72/297.04 , activate(X) -> X 627.72/297.04 , activate(n__0()) -> 0() 627.72/297.04 , activate(n__s(X)) -> s(activate(X)) 627.72/297.04 , activate(n__diff(X1, X2)) -> diff(activate(X1), activate(X2)) 627.72/297.04 , activate(n__p(X)) -> p(activate(X)) 627.72/297.04 , diff(X, Y) -> if(leq(X, Y), n__0(), n__s(n__diff(n__p(X), Y))) 627.72/297.04 , diff(X1, X2) -> n__diff(X1, X2) } 627.72/297.04 Obligation: 627.72/297.04 runtime complexity 627.72/297.04 Answer: 627.72/297.04 MAYBE 627.72/297.04 627.72/297.04 None of the processors succeeded. 627.72/297.04 627.72/297.04 Details of failed attempt(s): 627.72/297.04 ----------------------------- 627.72/297.04 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 627.72/297.04 following reason: 627.72/297.04 627.72/297.04 Computation stopped due to timeout after 297.0 seconds. 627.72/297.04 627.72/297.04 2) 'Best' failed due to the following reason: 627.72/297.04 627.72/297.04 None of the processors succeeded. 627.72/297.04 627.72/297.04 Details of failed attempt(s): 627.72/297.04 ----------------------------- 627.72/297.04 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 627.72/297.04 seconds)' failed due to the following reason: 627.72/297.04 627.72/297.04 None of the processors succeeded. 627.72/297.04 627.72/297.04 Details of failed attempt(s): 627.72/297.04 ----------------------------- 627.72/297.04 1) 'empty' failed due to the following reason: 627.72/297.04 627.72/297.04 Empty strict component of the problem is NOT empty. 627.72/297.04 627.72/297.04 2) 'With Problem ...' failed due to the following reason: 627.72/297.04 627.72/297.04 None of the processors succeeded. 627.72/297.04 627.72/297.04 Details of failed attempt(s): 627.72/297.04 ----------------------------- 627.72/297.04 1) 'empty' failed due to the following reason: 627.72/297.04 627.72/297.04 Empty strict component of the problem is NOT empty. 627.72/297.04 627.72/297.04 2) 'Fastest' failed due to the following reason: 627.72/297.04 627.72/297.04 None of the processors succeeded. 627.72/297.04 627.72/297.04 Details of failed attempt(s): 627.72/297.04 ----------------------------- 627.72/297.04 1) 'With Problem ...' failed due to the following reason: 627.72/297.04 627.72/297.04 None of the processors succeeded. 627.72/297.04 627.72/297.04 Details of failed attempt(s): 627.72/297.04 ----------------------------- 627.72/297.04 1) 'empty' failed due to the following reason: 627.72/297.04 627.72/297.04 Empty strict component of the problem is NOT empty. 627.72/297.04 627.72/297.04 2) 'With Problem ...' failed due to the following reason: 627.72/297.04 627.72/297.04 None of the processors succeeded. 627.72/297.04 627.72/297.04 Details of failed attempt(s): 627.72/297.04 ----------------------------- 627.72/297.04 1) 'empty' failed due to the following reason: 627.72/297.04 627.72/297.04 Empty strict component of the problem is NOT empty. 627.72/297.04 627.72/297.04 2) 'With Problem ...' failed due to the following reason: 627.72/297.04 627.72/297.04 None of the processors succeeded. 627.72/297.04 627.72/297.04 Details of failed attempt(s): 627.72/297.04 ----------------------------- 627.72/297.04 1) 'empty' failed due to the following reason: 627.72/297.04 627.72/297.04 Empty strict component of the problem is NOT empty. 627.72/297.04 627.72/297.04 2) 'With Problem ...' failed due to the following reason: 627.72/297.04 627.72/297.04 Empty strict component of the problem is NOT empty. 627.72/297.04 627.72/297.04 627.72/297.04 627.72/297.04 627.72/297.04 2) 'With Problem ...' failed due to the following reason: 627.72/297.04 627.72/297.04 None of the processors succeeded. 627.72/297.04 627.72/297.04 Details of failed attempt(s): 627.72/297.04 ----------------------------- 627.72/297.04 1) 'empty' failed due to the following reason: 627.72/297.04 627.72/297.04 Empty strict component of the problem is NOT empty. 627.72/297.04 627.72/297.04 2) 'With Problem ...' failed due to the following reason: 627.72/297.04 627.72/297.04 Empty strict component of the problem is NOT empty. 627.72/297.04 627.72/297.04 627.72/297.04 627.72/297.04 627.72/297.04 627.72/297.04 2) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 627.72/297.04 failed due to the following reason: 627.72/297.04 627.72/297.04 None of the processors succeeded. 627.72/297.04 627.72/297.04 Details of failed attempt(s): 627.72/297.04 ----------------------------- 627.72/297.04 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 627.72/297.04 failed due to the following reason: 627.72/297.04 627.72/297.04 match-boundness of the problem could not be verified. 627.72/297.04 627.72/297.04 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 627.72/297.04 failed due to the following reason: 627.72/297.04 627.72/297.04 match-boundness of the problem could not be verified. 627.72/297.04 627.72/297.04 627.72/297.04 3) 'Best' failed due to the following reason: 627.72/297.04 627.72/297.04 None of the processors succeeded. 627.72/297.04 627.72/297.04 Details of failed attempt(s): 627.72/297.04 ----------------------------- 627.72/297.04 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 627.72/297.04 following reason: 627.72/297.04 627.72/297.04 The processor is inapplicable, reason: 627.72/297.04 Processor only applicable for innermost runtime complexity analysis 627.72/297.04 627.72/297.04 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 627.72/297.04 to the following reason: 627.72/297.04 627.72/297.04 The processor is inapplicable, reason: 627.72/297.04 Processor only applicable for innermost runtime complexity analysis 627.72/297.04 627.72/297.04 627.72/297.04 627.72/297.04 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 627.72/297.04 the following reason: 627.72/297.04 627.72/297.04 We add the following weak dependency pairs: 627.72/297.04 627.72/297.04 Strict DPs: 627.72/297.04 { p^#(X) -> c_1(X) 627.72/297.04 , p^#(0()) -> c_2(0^#()) 627.72/297.04 , p^#(s(X)) -> c_3(X) 627.72/297.04 , 0^#() -> c_4() 627.72/297.04 , s^#(X) -> c_5(X) 627.72/297.04 , leq^#(0(), Y) -> c_6() 627.72/297.04 , leq^#(s(X), 0()) -> c_7() 627.72/297.04 , leq^#(s(X), s(Y)) -> c_8(leq^#(X, Y)) 627.72/297.04 , if^#(true(), X, Y) -> c_9(activate^#(X)) 627.72/297.04 , if^#(false(), X, Y) -> c_10(activate^#(Y)) 627.72/297.04 , activate^#(X) -> c_11(X) 627.72/297.04 , activate^#(n__0()) -> c_12(0^#()) 627.72/297.04 , activate^#(n__s(X)) -> c_13(s^#(activate(X))) 627.72/297.04 , activate^#(n__diff(X1, X2)) -> 627.72/297.04 c_14(diff^#(activate(X1), activate(X2))) 627.72/297.04 , activate^#(n__p(X)) -> c_15(p^#(activate(X))) 627.72/297.04 , diff^#(X, Y) -> 627.72/297.04 c_16(if^#(leq(X, Y), n__0(), n__s(n__diff(n__p(X), Y)))) 627.72/297.04 , diff^#(X1, X2) -> c_17(X1, X2) } 627.72/297.04 627.72/297.04 and mark the set of starting terms. 627.72/297.04 627.72/297.04 We are left with following problem, upon which TcT provides the 627.72/297.04 certificate MAYBE. 627.72/297.04 627.72/297.04 Strict DPs: 627.72/297.04 { p^#(X) -> c_1(X) 627.72/297.04 , p^#(0()) -> c_2(0^#()) 627.72/297.04 , p^#(s(X)) -> c_3(X) 627.72/297.04 , 0^#() -> c_4() 627.72/297.04 , s^#(X) -> c_5(X) 627.72/297.04 , leq^#(0(), Y) -> c_6() 627.72/297.04 , leq^#(s(X), 0()) -> c_7() 627.72/297.04 , leq^#(s(X), s(Y)) -> c_8(leq^#(X, Y)) 627.72/297.04 , if^#(true(), X, Y) -> c_9(activate^#(X)) 627.72/297.04 , if^#(false(), X, Y) -> c_10(activate^#(Y)) 627.72/297.04 , activate^#(X) -> c_11(X) 627.72/297.04 , activate^#(n__0()) -> c_12(0^#()) 627.72/297.04 , activate^#(n__s(X)) -> c_13(s^#(activate(X))) 627.72/297.04 , activate^#(n__diff(X1, X2)) -> 627.72/297.04 c_14(diff^#(activate(X1), activate(X2))) 627.72/297.04 , activate^#(n__p(X)) -> c_15(p^#(activate(X))) 627.72/297.04 , diff^#(X, Y) -> 627.72/297.04 c_16(if^#(leq(X, Y), n__0(), n__s(n__diff(n__p(X), Y)))) 627.72/297.04 , diff^#(X1, X2) -> c_17(X1, X2) } 627.72/297.04 Strict Trs: 627.72/297.04 { p(X) -> n__p(X) 627.72/297.04 , p(0()) -> 0() 627.72/297.04 , p(s(X)) -> X 627.72/297.04 , 0() -> n__0() 627.72/297.04 , s(X) -> n__s(X) 627.72/297.04 , leq(0(), Y) -> true() 627.72/297.04 , leq(s(X), 0()) -> false() 627.72/297.04 , leq(s(X), s(Y)) -> leq(X, Y) 627.72/297.04 , if(true(), X, Y) -> activate(X) 627.72/297.04 , if(false(), X, Y) -> activate(Y) 627.72/297.04 , activate(X) -> X 627.72/297.04 , activate(n__0()) -> 0() 627.72/297.04 , activate(n__s(X)) -> s(activate(X)) 627.72/297.04 , activate(n__diff(X1, X2)) -> diff(activate(X1), activate(X2)) 627.72/297.04 , activate(n__p(X)) -> p(activate(X)) 627.72/297.04 , diff(X, Y) -> if(leq(X, Y), n__0(), n__s(n__diff(n__p(X), Y))) 627.72/297.04 , diff(X1, X2) -> n__diff(X1, X2) } 627.72/297.04 Obligation: 627.72/297.04 runtime complexity 627.72/297.04 Answer: 627.72/297.04 MAYBE 627.72/297.04 627.72/297.04 We estimate the number of application of {4,6,7} by applications of 627.72/297.04 Pre({4,6,7}) = {1,2,3,5,8,11,12,17}. Here rules are labeled as 627.72/297.04 follows: 627.72/297.04 627.72/297.04 DPs: 627.72/297.04 { 1: p^#(X) -> c_1(X) 627.72/297.04 , 2: p^#(0()) -> c_2(0^#()) 627.72/297.04 , 3: p^#(s(X)) -> c_3(X) 627.72/297.04 , 4: 0^#() -> c_4() 627.72/297.04 , 5: s^#(X) -> c_5(X) 627.72/297.04 , 6: leq^#(0(), Y) -> c_6() 627.72/297.04 , 7: leq^#(s(X), 0()) -> c_7() 627.72/297.04 , 8: leq^#(s(X), s(Y)) -> c_8(leq^#(X, Y)) 627.72/297.04 , 9: if^#(true(), X, Y) -> c_9(activate^#(X)) 627.72/297.04 , 10: if^#(false(), X, Y) -> c_10(activate^#(Y)) 627.72/297.04 , 11: activate^#(X) -> c_11(X) 627.72/297.04 , 12: activate^#(n__0()) -> c_12(0^#()) 627.72/297.04 , 13: activate^#(n__s(X)) -> c_13(s^#(activate(X))) 627.72/297.04 , 14: activate^#(n__diff(X1, X2)) -> 627.72/297.04 c_14(diff^#(activate(X1), activate(X2))) 627.72/297.04 , 15: activate^#(n__p(X)) -> c_15(p^#(activate(X))) 627.72/297.04 , 16: diff^#(X, Y) -> 627.72/297.04 c_16(if^#(leq(X, Y), n__0(), n__s(n__diff(n__p(X), Y)))) 627.72/297.04 , 17: diff^#(X1, X2) -> c_17(X1, X2) } 627.72/297.04 627.72/297.04 We are left with following problem, upon which TcT provides the 627.72/297.04 certificate MAYBE. 627.72/297.04 627.72/297.04 Strict DPs: 627.72/297.04 { p^#(X) -> c_1(X) 627.72/297.04 , p^#(0()) -> c_2(0^#()) 627.72/297.04 , p^#(s(X)) -> c_3(X) 627.72/297.04 , s^#(X) -> c_5(X) 627.72/297.04 , leq^#(s(X), s(Y)) -> c_8(leq^#(X, Y)) 627.72/297.04 , if^#(true(), X, Y) -> c_9(activate^#(X)) 627.72/297.04 , if^#(false(), X, Y) -> c_10(activate^#(Y)) 627.72/297.04 , activate^#(X) -> c_11(X) 627.72/297.04 , activate^#(n__0()) -> c_12(0^#()) 627.72/297.04 , activate^#(n__s(X)) -> c_13(s^#(activate(X))) 627.72/297.04 , activate^#(n__diff(X1, X2)) -> 627.72/297.04 c_14(diff^#(activate(X1), activate(X2))) 627.72/297.04 , activate^#(n__p(X)) -> c_15(p^#(activate(X))) 627.72/297.04 , diff^#(X, Y) -> 627.72/297.04 c_16(if^#(leq(X, Y), n__0(), n__s(n__diff(n__p(X), Y)))) 627.72/297.04 , diff^#(X1, X2) -> c_17(X1, X2) } 627.72/297.04 Strict Trs: 627.72/297.04 { p(X) -> n__p(X) 627.72/297.04 , p(0()) -> 0() 627.72/297.04 , p(s(X)) -> X 627.72/297.04 , 0() -> n__0() 627.72/297.04 , s(X) -> n__s(X) 627.72/297.04 , leq(0(), Y) -> true() 627.72/297.04 , leq(s(X), 0()) -> false() 627.72/297.04 , leq(s(X), s(Y)) -> leq(X, Y) 627.72/297.04 , if(true(), X, Y) -> activate(X) 627.72/297.04 , if(false(), X, Y) -> activate(Y) 627.72/297.04 , activate(X) -> X 627.72/297.04 , activate(n__0()) -> 0() 627.72/297.04 , activate(n__s(X)) -> s(activate(X)) 627.72/297.04 , activate(n__diff(X1, X2)) -> diff(activate(X1), activate(X2)) 627.72/297.04 , activate(n__p(X)) -> p(activate(X)) 627.72/297.04 , diff(X, Y) -> if(leq(X, Y), n__0(), n__s(n__diff(n__p(X), Y))) 627.72/297.04 , diff(X1, X2) -> n__diff(X1, X2) } 627.72/297.04 Weak DPs: 627.72/297.04 { 0^#() -> c_4() 627.72/297.04 , leq^#(0(), Y) -> c_6() 627.72/297.04 , leq^#(s(X), 0()) -> c_7() } 627.72/297.04 Obligation: 627.72/297.04 runtime complexity 627.72/297.04 Answer: 627.72/297.04 MAYBE 627.72/297.04 627.72/297.04 We estimate the number of application of {2,9} by applications of 627.72/297.04 Pre({2,9}) = {1,3,4,6,7,8,12,14}. Here rules are labeled as 627.72/297.04 follows: 627.72/297.04 627.72/297.04 DPs: 627.72/297.04 { 1: p^#(X) -> c_1(X) 627.72/297.04 , 2: p^#(0()) -> c_2(0^#()) 627.72/297.04 , 3: p^#(s(X)) -> c_3(X) 627.72/297.04 , 4: s^#(X) -> c_5(X) 627.72/297.04 , 5: leq^#(s(X), s(Y)) -> c_8(leq^#(X, Y)) 627.72/297.04 , 6: if^#(true(), X, Y) -> c_9(activate^#(X)) 627.72/297.04 , 7: if^#(false(), X, Y) -> c_10(activate^#(Y)) 627.72/297.04 , 8: activate^#(X) -> c_11(X) 627.72/297.04 , 9: activate^#(n__0()) -> c_12(0^#()) 627.72/297.04 , 10: activate^#(n__s(X)) -> c_13(s^#(activate(X))) 627.72/297.04 , 11: activate^#(n__diff(X1, X2)) -> 627.72/297.04 c_14(diff^#(activate(X1), activate(X2))) 627.72/297.04 , 12: activate^#(n__p(X)) -> c_15(p^#(activate(X))) 627.72/297.04 , 13: diff^#(X, Y) -> 627.72/297.04 c_16(if^#(leq(X, Y), n__0(), n__s(n__diff(n__p(X), Y)))) 627.72/297.04 , 14: diff^#(X1, X2) -> c_17(X1, X2) 627.72/297.04 , 15: 0^#() -> c_4() 627.72/297.04 , 16: leq^#(0(), Y) -> c_6() 627.72/297.04 , 17: leq^#(s(X), 0()) -> c_7() } 627.72/297.04 627.72/297.04 We are left with following problem, upon which TcT provides the 627.72/297.04 certificate MAYBE. 627.72/297.04 627.72/297.04 Strict DPs: 627.72/297.04 { p^#(X) -> c_1(X) 627.72/297.04 , p^#(s(X)) -> c_3(X) 627.72/297.04 , s^#(X) -> c_5(X) 627.72/297.04 , leq^#(s(X), s(Y)) -> c_8(leq^#(X, Y)) 627.72/297.04 , if^#(true(), X, Y) -> c_9(activate^#(X)) 627.72/297.04 , if^#(false(), X, Y) -> c_10(activate^#(Y)) 627.72/297.04 , activate^#(X) -> c_11(X) 627.72/297.04 , activate^#(n__s(X)) -> c_13(s^#(activate(X))) 627.72/297.04 , activate^#(n__diff(X1, X2)) -> 627.72/297.04 c_14(diff^#(activate(X1), activate(X2))) 627.72/297.04 , activate^#(n__p(X)) -> c_15(p^#(activate(X))) 627.72/297.04 , diff^#(X, Y) -> 627.72/297.04 c_16(if^#(leq(X, Y), n__0(), n__s(n__diff(n__p(X), Y)))) 627.72/297.04 , diff^#(X1, X2) -> c_17(X1, X2) } 627.72/297.04 Strict Trs: 627.72/297.04 { p(X) -> n__p(X) 627.72/297.04 , p(0()) -> 0() 627.72/297.04 , p(s(X)) -> X 627.72/297.04 , 0() -> n__0() 627.72/297.04 , s(X) -> n__s(X) 627.72/297.04 , leq(0(), Y) -> true() 627.72/297.04 , leq(s(X), 0()) -> false() 627.72/297.04 , leq(s(X), s(Y)) -> leq(X, Y) 627.72/297.04 , if(true(), X, Y) -> activate(X) 627.72/297.04 , if(false(), X, Y) -> activate(Y) 627.72/297.04 , activate(X) -> X 627.72/297.04 , activate(n__0()) -> 0() 627.72/297.04 , activate(n__s(X)) -> s(activate(X)) 627.72/297.04 , activate(n__diff(X1, X2)) -> diff(activate(X1), activate(X2)) 627.72/297.04 , activate(n__p(X)) -> p(activate(X)) 627.72/297.04 , diff(X, Y) -> if(leq(X, Y), n__0(), n__s(n__diff(n__p(X), Y))) 627.72/297.04 , diff(X1, X2) -> n__diff(X1, X2) } 627.72/297.04 Weak DPs: 627.72/297.04 { p^#(0()) -> c_2(0^#()) 627.72/297.04 , 0^#() -> c_4() 627.72/297.04 , leq^#(0(), Y) -> c_6() 627.72/297.04 , leq^#(s(X), 0()) -> c_7() 627.72/297.04 , activate^#(n__0()) -> c_12(0^#()) } 627.72/297.04 Obligation: 627.72/297.04 runtime complexity 627.72/297.04 Answer: 627.72/297.04 MAYBE 627.72/297.04 627.72/297.04 Empty strict component of the problem is NOT empty. 627.72/297.04 627.72/297.04 627.72/297.04 Arrrr.. 628.04/297.31 EOF