MAYBE 817.23/297.03 MAYBE 817.23/297.03 817.23/297.03 We are left with following problem, upon which TcT provides the 817.23/297.03 certificate MAYBE. 817.23/297.03 817.23/297.03 Strict Trs: 817.23/297.03 { U11(tt(), N) -> activate(N) 817.23/297.03 , activate(X) -> X 817.23/297.03 , activate(n__0()) -> 0() 817.23/297.03 , activate(n__plus(X1, X2)) -> plus(X1, X2) 817.23/297.03 , activate(n__isNat(X)) -> isNat(X) 817.23/297.03 , activate(n__s(X)) -> s(X) 817.23/297.03 , U21(tt(), M, N) -> s(plus(activate(N), activate(M))) 817.23/297.03 , s(X) -> n__s(X) 817.23/297.03 , plus(X1, X2) -> n__plus(X1, X2) 817.23/297.03 , plus(N, s(M)) -> U21(and(isNat(M), n__isNat(N)), M, N) 817.23/297.03 , plus(N, 0()) -> U11(isNat(N), N) 817.23/297.03 , and(tt(), X) -> activate(X) 817.23/297.03 , isNat(X) -> n__isNat(X) 817.23/297.03 , isNat(n__0()) -> tt() 817.23/297.03 , isNat(n__plus(V1, V2)) -> 817.23/297.03 and(isNat(activate(V1)), n__isNat(activate(V2))) 817.23/297.03 , isNat(n__s(V1)) -> isNat(activate(V1)) 817.23/297.03 , 0() -> n__0() } 817.23/297.03 Obligation: 817.23/297.03 runtime complexity 817.23/297.03 Answer: 817.23/297.03 MAYBE 817.23/297.03 817.23/297.03 None of the processors succeeded. 817.23/297.03 817.23/297.03 Details of failed attempt(s): 817.23/297.03 ----------------------------- 817.23/297.03 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 817.23/297.03 following reason: 817.23/297.03 817.23/297.03 Computation stopped due to timeout after 297.0 seconds. 817.23/297.03 817.23/297.03 2) 'Best' failed due to the following reason: 817.23/297.03 817.23/297.03 None of the processors succeeded. 817.23/297.03 817.23/297.03 Details of failed attempt(s): 817.23/297.03 ----------------------------- 817.23/297.03 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 817.23/297.03 seconds)' failed due to the following reason: 817.23/297.03 817.23/297.03 Computation stopped due to timeout after 148.0 seconds. 817.23/297.03 817.23/297.03 2) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 817.23/297.03 failed due to the following reason: 817.23/297.03 817.23/297.03 None of the processors succeeded. 817.23/297.03 817.23/297.03 Details of failed attempt(s): 817.23/297.03 ----------------------------- 817.23/297.03 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 817.23/297.03 failed due to the following reason: 817.23/297.03 817.23/297.03 match-boundness of the problem could not be verified. 817.23/297.03 817.23/297.03 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 817.23/297.03 failed due to the following reason: 817.23/297.03 817.23/297.03 match-boundness of the problem could not be verified. 817.23/297.03 817.23/297.03 817.23/297.03 3) 'Best' failed due to the following reason: 817.23/297.03 817.23/297.03 None of the processors succeeded. 817.23/297.03 817.23/297.03 Details of failed attempt(s): 817.23/297.03 ----------------------------- 817.23/297.03 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 817.23/297.03 following reason: 817.23/297.03 817.23/297.03 The processor is inapplicable, reason: 817.23/297.03 Processor only applicable for innermost runtime complexity analysis 817.23/297.03 817.23/297.03 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 817.23/297.03 to the following reason: 817.23/297.03 817.23/297.03 The processor is inapplicable, reason: 817.23/297.03 Processor only applicable for innermost runtime complexity analysis 817.23/297.03 817.23/297.03 817.23/297.03 817.23/297.03 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 817.23/297.03 the following reason: 817.23/297.03 817.23/297.03 We add the following weak dependency pairs: 817.23/297.03 817.23/297.03 Strict DPs: 817.23/297.03 { U11^#(tt(), N) -> c_1(activate^#(N)) 817.23/297.03 , activate^#(X) -> c_2(X) 817.23/297.03 , activate^#(n__0()) -> c_3(0^#()) 817.23/297.03 , activate^#(n__plus(X1, X2)) -> c_4(plus^#(X1, X2)) 817.23/297.03 , activate^#(n__isNat(X)) -> c_5(isNat^#(X)) 817.23/297.03 , activate^#(n__s(X)) -> c_6(s^#(X)) 817.23/297.03 , 0^#() -> c_17() 817.23/297.03 , plus^#(X1, X2) -> c_9(X1, X2) 817.23/297.03 , plus^#(N, s(M)) -> c_10(U21^#(and(isNat(M), n__isNat(N)), M, N)) 817.23/297.03 , plus^#(N, 0()) -> c_11(U11^#(isNat(N), N)) 817.23/297.03 , isNat^#(X) -> c_13(X) 817.23/297.03 , isNat^#(n__0()) -> c_14() 817.23/297.03 , isNat^#(n__plus(V1, V2)) -> 817.23/297.03 c_15(and^#(isNat(activate(V1)), n__isNat(activate(V2)))) 817.23/297.03 , isNat^#(n__s(V1)) -> c_16(isNat^#(activate(V1))) 817.23/297.03 , s^#(X) -> c_8(X) 817.23/297.03 , U21^#(tt(), M, N) -> c_7(s^#(plus(activate(N), activate(M)))) 817.23/297.03 , and^#(tt(), X) -> c_12(activate^#(X)) } 817.23/297.03 817.23/297.03 and mark the set of starting terms. 817.23/297.03 817.23/297.03 We are left with following problem, upon which TcT provides the 817.23/297.03 certificate MAYBE. 817.23/297.03 817.23/297.03 Strict DPs: 817.23/297.03 { U11^#(tt(), N) -> c_1(activate^#(N)) 817.23/297.03 , activate^#(X) -> c_2(X) 817.23/297.03 , activate^#(n__0()) -> c_3(0^#()) 817.23/297.03 , activate^#(n__plus(X1, X2)) -> c_4(plus^#(X1, X2)) 817.23/297.03 , activate^#(n__isNat(X)) -> c_5(isNat^#(X)) 817.23/297.03 , activate^#(n__s(X)) -> c_6(s^#(X)) 817.23/297.03 , 0^#() -> c_17() 817.23/297.03 , plus^#(X1, X2) -> c_9(X1, X2) 817.23/297.03 , plus^#(N, s(M)) -> c_10(U21^#(and(isNat(M), n__isNat(N)), M, N)) 817.23/297.03 , plus^#(N, 0()) -> c_11(U11^#(isNat(N), N)) 817.23/297.03 , isNat^#(X) -> c_13(X) 817.23/297.03 , isNat^#(n__0()) -> c_14() 817.23/297.03 , isNat^#(n__plus(V1, V2)) -> 817.23/297.03 c_15(and^#(isNat(activate(V1)), n__isNat(activate(V2)))) 817.23/297.03 , isNat^#(n__s(V1)) -> c_16(isNat^#(activate(V1))) 817.23/297.03 , s^#(X) -> c_8(X) 817.23/297.03 , U21^#(tt(), M, N) -> c_7(s^#(plus(activate(N), activate(M)))) 817.23/297.03 , and^#(tt(), X) -> c_12(activate^#(X)) } 817.23/297.03 Strict Trs: 817.23/297.03 { U11(tt(), N) -> activate(N) 817.23/297.03 , activate(X) -> X 817.23/297.03 , activate(n__0()) -> 0() 817.23/297.03 , activate(n__plus(X1, X2)) -> plus(X1, X2) 817.23/297.03 , activate(n__isNat(X)) -> isNat(X) 817.23/297.03 , activate(n__s(X)) -> s(X) 817.23/297.03 , U21(tt(), M, N) -> s(plus(activate(N), activate(M))) 817.23/297.03 , s(X) -> n__s(X) 817.23/297.03 , plus(X1, X2) -> n__plus(X1, X2) 817.23/297.03 , plus(N, s(M)) -> U21(and(isNat(M), n__isNat(N)), M, N) 817.23/297.03 , plus(N, 0()) -> U11(isNat(N), N) 817.23/297.03 , and(tt(), X) -> activate(X) 817.23/297.03 , isNat(X) -> n__isNat(X) 817.23/297.03 , isNat(n__0()) -> tt() 817.23/297.03 , isNat(n__plus(V1, V2)) -> 817.23/297.03 and(isNat(activate(V1)), n__isNat(activate(V2))) 817.23/297.03 , isNat(n__s(V1)) -> isNat(activate(V1)) 817.23/297.03 , 0() -> n__0() } 817.23/297.03 Obligation: 817.23/297.03 runtime complexity 817.23/297.03 Answer: 817.23/297.03 MAYBE 817.23/297.03 817.23/297.03 We estimate the number of application of {7,12} by applications of 817.23/297.03 Pre({7,12}) = {2,3,5,8,11,14,15}. Here rules are labeled as 817.23/297.03 follows: 817.23/297.03 817.23/297.03 DPs: 817.23/297.03 { 1: U11^#(tt(), N) -> c_1(activate^#(N)) 817.23/297.03 , 2: activate^#(X) -> c_2(X) 817.23/297.03 , 3: activate^#(n__0()) -> c_3(0^#()) 817.23/297.03 , 4: activate^#(n__plus(X1, X2)) -> c_4(plus^#(X1, X2)) 817.23/297.03 , 5: activate^#(n__isNat(X)) -> c_5(isNat^#(X)) 817.23/297.03 , 6: activate^#(n__s(X)) -> c_6(s^#(X)) 817.23/297.03 , 7: 0^#() -> c_17() 817.23/297.03 , 8: plus^#(X1, X2) -> c_9(X1, X2) 817.23/297.03 , 9: plus^#(N, s(M)) -> 817.23/297.03 c_10(U21^#(and(isNat(M), n__isNat(N)), M, N)) 817.23/297.03 , 10: plus^#(N, 0()) -> c_11(U11^#(isNat(N), N)) 817.23/297.03 , 11: isNat^#(X) -> c_13(X) 817.23/297.03 , 12: isNat^#(n__0()) -> c_14() 817.23/297.03 , 13: isNat^#(n__plus(V1, V2)) -> 817.23/297.03 c_15(and^#(isNat(activate(V1)), n__isNat(activate(V2)))) 817.23/297.03 , 14: isNat^#(n__s(V1)) -> c_16(isNat^#(activate(V1))) 817.23/297.03 , 15: s^#(X) -> c_8(X) 817.23/297.03 , 16: U21^#(tt(), M, N) -> c_7(s^#(plus(activate(N), activate(M)))) 817.23/297.03 , 17: and^#(tt(), X) -> c_12(activate^#(X)) } 817.23/297.03 817.23/297.03 We are left with following problem, upon which TcT provides the 817.23/297.03 certificate MAYBE. 817.23/297.03 817.23/297.03 Strict DPs: 817.23/297.03 { U11^#(tt(), N) -> c_1(activate^#(N)) 817.23/297.03 , activate^#(X) -> c_2(X) 817.23/297.03 , activate^#(n__0()) -> c_3(0^#()) 817.23/297.03 , activate^#(n__plus(X1, X2)) -> c_4(plus^#(X1, X2)) 817.23/297.03 , activate^#(n__isNat(X)) -> c_5(isNat^#(X)) 817.23/297.03 , activate^#(n__s(X)) -> c_6(s^#(X)) 817.23/297.03 , plus^#(X1, X2) -> c_9(X1, X2) 817.23/297.03 , plus^#(N, s(M)) -> c_10(U21^#(and(isNat(M), n__isNat(N)), M, N)) 817.23/297.03 , plus^#(N, 0()) -> c_11(U11^#(isNat(N), N)) 817.23/297.03 , isNat^#(X) -> c_13(X) 817.23/297.03 , isNat^#(n__plus(V1, V2)) -> 817.23/297.03 c_15(and^#(isNat(activate(V1)), n__isNat(activate(V2)))) 817.23/297.03 , isNat^#(n__s(V1)) -> c_16(isNat^#(activate(V1))) 817.23/297.03 , s^#(X) -> c_8(X) 817.23/297.03 , U21^#(tt(), M, N) -> c_7(s^#(plus(activate(N), activate(M)))) 817.23/297.03 , and^#(tt(), X) -> c_12(activate^#(X)) } 817.23/297.03 Strict Trs: 817.23/297.03 { U11(tt(), N) -> activate(N) 817.23/297.03 , activate(X) -> X 817.23/297.03 , activate(n__0()) -> 0() 817.23/297.03 , activate(n__plus(X1, X2)) -> plus(X1, X2) 817.23/297.03 , activate(n__isNat(X)) -> isNat(X) 817.23/297.03 , activate(n__s(X)) -> s(X) 817.23/297.03 , U21(tt(), M, N) -> s(plus(activate(N), activate(M))) 817.23/297.03 , s(X) -> n__s(X) 817.23/297.03 , plus(X1, X2) -> n__plus(X1, X2) 817.23/297.03 , plus(N, s(M)) -> U21(and(isNat(M), n__isNat(N)), M, N) 817.23/297.03 , plus(N, 0()) -> U11(isNat(N), N) 817.23/297.03 , and(tt(), X) -> activate(X) 817.23/297.03 , isNat(X) -> n__isNat(X) 817.23/297.03 , isNat(n__0()) -> tt() 817.23/297.03 , isNat(n__plus(V1, V2)) -> 817.23/297.03 and(isNat(activate(V1)), n__isNat(activate(V2))) 817.23/297.03 , isNat(n__s(V1)) -> isNat(activate(V1)) 817.23/297.03 , 0() -> n__0() } 817.23/297.03 Weak DPs: 817.23/297.03 { 0^#() -> c_17() 817.23/297.03 , isNat^#(n__0()) -> c_14() } 817.23/297.03 Obligation: 817.23/297.03 runtime complexity 817.23/297.03 Answer: 817.23/297.03 MAYBE 817.23/297.03 817.23/297.03 We estimate the number of application of {3} by applications of 817.23/297.03 Pre({3}) = {1,2,7,10,13,15}. Here rules are labeled as follows: 817.23/297.03 817.23/297.03 DPs: 817.23/297.03 { 1: U11^#(tt(), N) -> c_1(activate^#(N)) 817.23/297.03 , 2: activate^#(X) -> c_2(X) 817.23/297.03 , 3: activate^#(n__0()) -> c_3(0^#()) 817.23/297.03 , 4: activate^#(n__plus(X1, X2)) -> c_4(plus^#(X1, X2)) 817.23/297.03 , 5: activate^#(n__isNat(X)) -> c_5(isNat^#(X)) 817.23/297.03 , 6: activate^#(n__s(X)) -> c_6(s^#(X)) 817.23/297.03 , 7: plus^#(X1, X2) -> c_9(X1, X2) 817.23/297.03 , 8: plus^#(N, s(M)) -> 817.23/297.03 c_10(U21^#(and(isNat(M), n__isNat(N)), M, N)) 817.23/297.03 , 9: plus^#(N, 0()) -> c_11(U11^#(isNat(N), N)) 817.23/297.03 , 10: isNat^#(X) -> c_13(X) 817.23/297.03 , 11: isNat^#(n__plus(V1, V2)) -> 817.23/297.03 c_15(and^#(isNat(activate(V1)), n__isNat(activate(V2)))) 817.23/297.03 , 12: isNat^#(n__s(V1)) -> c_16(isNat^#(activate(V1))) 817.23/297.03 , 13: s^#(X) -> c_8(X) 817.23/297.03 , 14: U21^#(tt(), M, N) -> c_7(s^#(plus(activate(N), activate(M)))) 817.23/297.03 , 15: and^#(tt(), X) -> c_12(activate^#(X)) 817.23/297.03 , 16: 0^#() -> c_17() 817.23/297.03 , 17: isNat^#(n__0()) -> c_14() } 817.23/297.03 817.23/297.03 We are left with following problem, upon which TcT provides the 817.23/297.03 certificate MAYBE. 817.23/297.03 817.23/297.03 Strict DPs: 817.23/297.03 { U11^#(tt(), N) -> c_1(activate^#(N)) 817.23/297.03 , activate^#(X) -> c_2(X) 817.23/297.03 , activate^#(n__plus(X1, X2)) -> c_4(plus^#(X1, X2)) 817.23/297.03 , activate^#(n__isNat(X)) -> c_5(isNat^#(X)) 817.23/297.03 , activate^#(n__s(X)) -> c_6(s^#(X)) 817.23/297.03 , plus^#(X1, X2) -> c_9(X1, X2) 817.23/297.03 , plus^#(N, s(M)) -> c_10(U21^#(and(isNat(M), n__isNat(N)), M, N)) 817.23/297.03 , plus^#(N, 0()) -> c_11(U11^#(isNat(N), N)) 817.23/297.03 , isNat^#(X) -> c_13(X) 817.23/297.03 , isNat^#(n__plus(V1, V2)) -> 817.23/297.03 c_15(and^#(isNat(activate(V1)), n__isNat(activate(V2)))) 817.23/297.03 , isNat^#(n__s(V1)) -> c_16(isNat^#(activate(V1))) 817.23/297.03 , s^#(X) -> c_8(X) 817.23/297.03 , U21^#(tt(), M, N) -> c_7(s^#(plus(activate(N), activate(M)))) 817.23/297.03 , and^#(tt(), X) -> c_12(activate^#(X)) } 817.23/297.03 Strict Trs: 817.23/297.03 { U11(tt(), N) -> activate(N) 817.23/297.03 , activate(X) -> X 817.23/297.03 , activate(n__0()) -> 0() 817.23/297.03 , activate(n__plus(X1, X2)) -> plus(X1, X2) 817.23/297.03 , activate(n__isNat(X)) -> isNat(X) 817.23/297.03 , activate(n__s(X)) -> s(X) 817.23/297.03 , U21(tt(), M, N) -> s(plus(activate(N), activate(M))) 817.23/297.03 , s(X) -> n__s(X) 817.23/297.03 , plus(X1, X2) -> n__plus(X1, X2) 817.23/297.03 , plus(N, s(M)) -> U21(and(isNat(M), n__isNat(N)), M, N) 817.23/297.03 , plus(N, 0()) -> U11(isNat(N), N) 817.23/297.03 , and(tt(), X) -> activate(X) 817.23/297.03 , isNat(X) -> n__isNat(X) 817.23/297.03 , isNat(n__0()) -> tt() 817.23/297.03 , isNat(n__plus(V1, V2)) -> 817.23/297.03 and(isNat(activate(V1)), n__isNat(activate(V2))) 817.23/297.03 , isNat(n__s(V1)) -> isNat(activate(V1)) 817.23/297.03 , 0() -> n__0() } 817.23/297.03 Weak DPs: 817.23/297.03 { activate^#(n__0()) -> c_3(0^#()) 817.23/297.03 , 0^#() -> c_17() 817.23/297.03 , isNat^#(n__0()) -> c_14() } 817.23/297.03 Obligation: 817.23/297.03 runtime complexity 817.23/297.03 Answer: 817.23/297.03 MAYBE 817.23/297.03 817.23/297.03 Empty strict component of the problem is NOT empty. 817.23/297.03 817.23/297.03 817.23/297.03 Arrrr.. 817.45/297.22 EOF