MAYBE 1184.36/297.08 MAYBE 1184.36/297.08 1184.36/297.08 We are left with following problem, upon which TcT provides the 1184.36/297.08 certificate MAYBE. 1184.36/297.08 1184.36/297.08 Strict Trs: 1184.36/297.08 { +(x, 0()) -> x 1184.36/297.08 , +(+(x, y), z) -> +(x, +(y, z)) 1184.36/297.08 , +(0(), x) -> x 1184.36/297.08 , +(s(x), s(y)) -> s(s(+(x, y))) 1184.36/297.08 , *(x, 0()) -> 0() 1184.36/297.08 , *(0(), x) -> 0() 1184.36/297.08 , *(s(x), s(y)) -> s(+(*(x, y), +(x, y))) 1184.36/297.08 , *(*(x, y), z) -> *(x, *(y, z)) 1184.36/297.08 , sum(nil()) -> 0() 1184.36/297.08 , sum(cons(x, l)) -> +(x, sum(l)) 1184.36/297.08 , prod(nil()) -> s(0()) 1184.36/297.08 , prod(cons(x, l)) -> *(x, prod(l)) } 1184.36/297.08 Obligation: 1184.36/297.08 runtime complexity 1184.36/297.08 Answer: 1184.36/297.08 MAYBE 1184.36/297.08 1184.36/297.08 None of the processors succeeded. 1184.36/297.08 1184.36/297.08 Details of failed attempt(s): 1184.36/297.08 ----------------------------- 1184.36/297.08 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 1184.36/297.08 following reason: 1184.36/297.08 1184.36/297.08 Computation stopped due to timeout after 297.0 seconds. 1184.36/297.08 1184.36/297.08 2) 'Best' failed due to the following reason: 1184.36/297.08 1184.36/297.08 None of the processors succeeded. 1184.36/297.08 1184.36/297.08 Details of failed attempt(s): 1184.36/297.08 ----------------------------- 1184.36/297.08 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 1184.36/297.08 seconds)' failed due to the following reason: 1184.36/297.08 1184.36/297.08 None of the processors succeeded. 1184.36/297.08 1184.36/297.08 Details of failed attempt(s): 1184.36/297.08 ----------------------------- 1184.36/297.08 1) 'empty' failed due to the following reason: 1184.36/297.08 1184.36/297.08 Empty strict component of the problem is NOT empty. 1184.36/297.08 1184.36/297.08 2) 'With Problem ...' failed due to the following reason: 1184.36/297.08 1184.36/297.08 None of the processors succeeded. 1184.36/297.08 1184.36/297.08 Details of failed attempt(s): 1184.36/297.08 ----------------------------- 1184.36/297.08 1) 'empty' failed due to the following reason: 1184.36/297.08 1184.36/297.08 Empty strict component of the problem is NOT empty. 1184.36/297.08 1184.36/297.08 2) 'Fastest' failed due to the following reason: 1184.36/297.08 1184.36/297.08 None of the processors succeeded. 1184.36/297.08 1184.36/297.08 Details of failed attempt(s): 1184.36/297.08 ----------------------------- 1184.36/297.08 1) 'With Problem ...' failed due to the following reason: 1184.36/297.08 1184.36/297.08 None of the processors succeeded. 1184.36/297.08 1184.36/297.08 Details of failed attempt(s): 1184.36/297.08 ----------------------------- 1184.36/297.08 1) 'empty' failed due to the following reason: 1184.36/297.08 1184.36/297.08 Empty strict component of the problem is NOT empty. 1184.36/297.08 1184.36/297.08 2) 'With Problem ...' failed due to the following reason: 1184.36/297.08 1184.36/297.08 None of the processors succeeded. 1184.36/297.08 1184.36/297.08 Details of failed attempt(s): 1184.36/297.08 ----------------------------- 1184.36/297.08 1) 'empty' failed due to the following reason: 1184.36/297.08 1184.36/297.08 Empty strict component of the problem is NOT empty. 1184.36/297.08 1184.36/297.08 2) 'With Problem ...' failed due to the following reason: 1184.36/297.08 1184.36/297.08 None of the processors succeeded. 1184.36/297.08 1184.36/297.08 Details of failed attempt(s): 1184.36/297.08 ----------------------------- 1184.36/297.08 1) 'empty' failed due to the following reason: 1184.36/297.08 1184.36/297.08 Empty strict component of the problem is NOT empty. 1184.36/297.08 1184.36/297.08 2) 'With Problem ...' failed due to the following reason: 1184.36/297.08 1184.36/297.08 Empty strict component of the problem is NOT empty. 1184.36/297.08 1184.36/297.08 1184.36/297.08 1184.36/297.08 1184.36/297.08 2) 'With Problem ...' failed due to the following reason: 1184.36/297.08 1184.36/297.08 None of the processors succeeded. 1184.36/297.08 1184.36/297.08 Details of failed attempt(s): 1184.36/297.08 ----------------------------- 1184.36/297.08 1) 'empty' failed due to the following reason: 1184.36/297.08 1184.36/297.08 Empty strict component of the problem is NOT empty. 1184.36/297.08 1184.36/297.08 2) 'With Problem ...' failed due to the following reason: 1184.36/297.08 1184.36/297.08 Empty strict component of the problem is NOT empty. 1184.36/297.08 1184.36/297.08 1184.36/297.08 1184.36/297.08 1184.36/297.08 1184.36/297.08 2) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 1184.36/297.08 failed due to the following reason: 1184.36/297.08 1184.36/297.08 None of the processors succeeded. 1184.36/297.08 1184.36/297.08 Details of failed attempt(s): 1184.36/297.08 ----------------------------- 1184.36/297.08 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 1184.36/297.08 failed due to the following reason: 1184.36/297.08 1184.36/297.08 match-boundness of the problem could not be verified. 1184.36/297.08 1184.36/297.08 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 1184.36/297.08 failed due to the following reason: 1184.36/297.08 1184.36/297.08 match-boundness of the problem could not be verified. 1184.36/297.08 1184.36/297.08 1184.36/297.08 3) 'Best' failed due to the following reason: 1184.36/297.08 1184.36/297.08 None of the processors succeeded. 1184.36/297.08 1184.36/297.08 Details of failed attempt(s): 1184.36/297.08 ----------------------------- 1184.36/297.08 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 1184.36/297.08 following reason: 1184.36/297.08 1184.36/297.08 The processor is inapplicable, reason: 1184.36/297.08 Processor only applicable for innermost runtime complexity analysis 1184.36/297.08 1184.36/297.08 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 1184.36/297.08 to the following reason: 1184.36/297.08 1184.36/297.08 The processor is inapplicable, reason: 1184.36/297.08 Processor only applicable for innermost runtime complexity analysis 1184.36/297.08 1184.36/297.08 1184.36/297.08 1184.36/297.08 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 1184.36/297.08 the following reason: 1184.36/297.08 1184.36/297.08 We add the following weak dependency pairs: 1184.36/297.08 1184.36/297.08 Strict DPs: 1184.36/297.08 { +^#(x, 0()) -> c_1(x) 1184.36/297.08 , +^#(+(x, y), z) -> c_2(+^#(x, +(y, z))) 1184.36/297.08 , +^#(0(), x) -> c_3(x) 1184.36/297.08 , +^#(s(x), s(y)) -> c_4(+^#(x, y)) 1184.36/297.08 , *^#(x, 0()) -> c_5() 1184.36/297.08 , *^#(0(), x) -> c_6() 1184.36/297.08 , *^#(s(x), s(y)) -> c_7(+^#(*(x, y), +(x, y))) 1184.36/297.08 , *^#(*(x, y), z) -> c_8(*^#(x, *(y, z))) 1184.36/297.08 , sum^#(nil()) -> c_9() 1184.36/297.08 , sum^#(cons(x, l)) -> c_10(+^#(x, sum(l))) 1184.36/297.08 , prod^#(nil()) -> c_11() 1184.36/297.08 , prod^#(cons(x, l)) -> c_12(*^#(x, prod(l))) } 1184.36/297.08 1184.36/297.08 and mark the set of starting terms. 1184.36/297.08 1184.36/297.08 We are left with following problem, upon which TcT provides the 1184.36/297.08 certificate MAYBE. 1184.36/297.08 1184.36/297.08 Strict DPs: 1184.36/297.08 { +^#(x, 0()) -> c_1(x) 1184.36/297.08 , +^#(+(x, y), z) -> c_2(+^#(x, +(y, z))) 1184.36/297.08 , +^#(0(), x) -> c_3(x) 1184.36/297.08 , +^#(s(x), s(y)) -> c_4(+^#(x, y)) 1184.36/297.08 , *^#(x, 0()) -> c_5() 1184.36/297.08 , *^#(0(), x) -> c_6() 1184.36/297.08 , *^#(s(x), s(y)) -> c_7(+^#(*(x, y), +(x, y))) 1184.36/297.08 , *^#(*(x, y), z) -> c_8(*^#(x, *(y, z))) 1184.36/297.08 , sum^#(nil()) -> c_9() 1184.36/297.08 , sum^#(cons(x, l)) -> c_10(+^#(x, sum(l))) 1184.36/297.08 , prod^#(nil()) -> c_11() 1184.36/297.08 , prod^#(cons(x, l)) -> c_12(*^#(x, prod(l))) } 1184.36/297.08 Strict Trs: 1184.36/297.08 { +(x, 0()) -> x 1184.36/297.08 , +(+(x, y), z) -> +(x, +(y, z)) 1184.36/297.08 , +(0(), x) -> x 1184.36/297.08 , +(s(x), s(y)) -> s(s(+(x, y))) 1184.36/297.08 , *(x, 0()) -> 0() 1184.36/297.08 , *(0(), x) -> 0() 1184.36/297.08 , *(s(x), s(y)) -> s(+(*(x, y), +(x, y))) 1184.36/297.08 , *(*(x, y), z) -> *(x, *(y, z)) 1184.36/297.08 , sum(nil()) -> 0() 1184.36/297.08 , sum(cons(x, l)) -> +(x, sum(l)) 1184.36/297.08 , prod(nil()) -> s(0()) 1184.36/297.08 , prod(cons(x, l)) -> *(x, prod(l)) } 1184.36/297.08 Obligation: 1184.36/297.08 runtime complexity 1184.36/297.08 Answer: 1184.36/297.08 MAYBE 1184.36/297.08 1184.36/297.08 We estimate the number of application of {5,6,9,11} by applications 1184.36/297.08 of Pre({5,6,9,11}) = {1,3,8,12}. Here rules are labeled as follows: 1184.36/297.08 1184.36/297.08 DPs: 1184.36/297.08 { 1: +^#(x, 0()) -> c_1(x) 1184.36/297.08 , 2: +^#(+(x, y), z) -> c_2(+^#(x, +(y, z))) 1184.36/297.08 , 3: +^#(0(), x) -> c_3(x) 1184.36/297.08 , 4: +^#(s(x), s(y)) -> c_4(+^#(x, y)) 1184.36/297.08 , 5: *^#(x, 0()) -> c_5() 1184.36/297.08 , 6: *^#(0(), x) -> c_6() 1184.36/297.08 , 7: *^#(s(x), s(y)) -> c_7(+^#(*(x, y), +(x, y))) 1184.36/297.08 , 8: *^#(*(x, y), z) -> c_8(*^#(x, *(y, z))) 1184.36/297.08 , 9: sum^#(nil()) -> c_9() 1184.36/297.08 , 10: sum^#(cons(x, l)) -> c_10(+^#(x, sum(l))) 1184.36/297.08 , 11: prod^#(nil()) -> c_11() 1184.36/297.08 , 12: prod^#(cons(x, l)) -> c_12(*^#(x, prod(l))) } 1184.36/297.08 1184.36/297.08 We are left with following problem, upon which TcT provides the 1184.36/297.08 certificate MAYBE. 1184.36/297.08 1184.36/297.08 Strict DPs: 1184.36/297.08 { +^#(x, 0()) -> c_1(x) 1184.36/297.08 , +^#(+(x, y), z) -> c_2(+^#(x, +(y, z))) 1184.36/297.08 , +^#(0(), x) -> c_3(x) 1184.36/297.08 , +^#(s(x), s(y)) -> c_4(+^#(x, y)) 1184.36/297.08 , *^#(s(x), s(y)) -> c_7(+^#(*(x, y), +(x, y))) 1184.36/297.08 , *^#(*(x, y), z) -> c_8(*^#(x, *(y, z))) 1184.36/297.08 , sum^#(cons(x, l)) -> c_10(+^#(x, sum(l))) 1184.36/297.08 , prod^#(cons(x, l)) -> c_12(*^#(x, prod(l))) } 1184.36/297.08 Strict Trs: 1184.36/297.09 { +(x, 0()) -> x 1184.36/297.09 , +(+(x, y), z) -> +(x, +(y, z)) 1184.36/297.09 , +(0(), x) -> x 1184.36/297.09 , +(s(x), s(y)) -> s(s(+(x, y))) 1184.36/297.09 , *(x, 0()) -> 0() 1184.36/297.09 , *(0(), x) -> 0() 1184.36/297.09 , *(s(x), s(y)) -> s(+(*(x, y), +(x, y))) 1184.36/297.09 , *(*(x, y), z) -> *(x, *(y, z)) 1184.36/297.09 , sum(nil()) -> 0() 1184.36/297.09 , sum(cons(x, l)) -> +(x, sum(l)) 1184.36/297.09 , prod(nil()) -> s(0()) 1184.36/297.09 , prod(cons(x, l)) -> *(x, prod(l)) } 1184.36/297.09 Weak DPs: 1184.36/297.09 { *^#(x, 0()) -> c_5() 1184.36/297.09 , *^#(0(), x) -> c_6() 1184.36/297.09 , sum^#(nil()) -> c_9() 1184.36/297.09 , prod^#(nil()) -> c_11() } 1184.36/297.09 Obligation: 1184.36/297.09 runtime complexity 1184.36/297.09 Answer: 1184.36/297.09 MAYBE 1184.36/297.09 1184.36/297.09 Empty strict component of the problem is NOT empty. 1184.36/297.09 1184.36/297.09 1184.36/297.09 Arrrr.. 1185.19/297.67 EOF