MAYBE 769.62/297.03 MAYBE 769.62/297.03 769.62/297.03 We are left with following problem, upon which TcT provides the 769.62/297.03 certificate MAYBE. 769.62/297.03 769.62/297.03 Strict Trs: 769.62/297.03 { 0(#()) -> #() 769.62/297.03 , +(x, #()) -> x 769.62/297.03 , +(0(x), 0(y)) -> 0(+(x, y)) 769.62/297.03 , +(0(x), 1(y)) -> 1(+(x, y)) 769.62/297.03 , +(#(), x) -> x 769.62/297.03 , +(+(x, y), z) -> +(x, +(y, z)) 769.62/297.03 , +(1(x), 0(y)) -> 1(+(x, y)) 769.62/297.03 , +(1(x), 1(y)) -> 0(+(+(x, y), 1(#()))) 769.62/297.03 , *(0(x), y) -> 0(*(x, y)) 769.62/297.03 , *(#(), x) -> #() 769.62/297.03 , *(1(x), y) -> +(0(*(x, y)), y) 769.62/297.03 , *(*(x, y), z) -> *(x, *(y, z)) 769.62/297.03 , sum(nil()) -> 0(#()) 769.62/297.03 , sum(cons(x, l)) -> +(x, sum(l)) 769.62/297.03 , prod(nil()) -> 1(#()) 769.62/297.03 , prod(cons(x, l)) -> *(x, prod(l)) } 769.62/297.03 Obligation: 769.62/297.03 runtime complexity 769.62/297.03 Answer: 769.62/297.03 MAYBE 769.62/297.03 769.62/297.03 None of the processors succeeded. 769.62/297.03 769.62/297.03 Details of failed attempt(s): 769.62/297.03 ----------------------------- 769.62/297.03 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 769.62/297.03 following reason: 769.62/297.03 769.62/297.03 Computation stopped due to timeout after 297.0 seconds. 769.62/297.03 769.62/297.03 2) 'Best' failed due to the following reason: 769.62/297.03 769.62/297.03 None of the processors succeeded. 769.62/297.03 769.62/297.03 Details of failed attempt(s): 769.62/297.03 ----------------------------- 769.62/297.03 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 769.62/297.03 seconds)' failed due to the following reason: 769.62/297.03 769.62/297.03 Computation stopped due to timeout after 148.0 seconds. 769.62/297.03 769.62/297.03 2) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 769.62/297.03 failed due to the following reason: 769.62/297.03 769.62/297.03 None of the processors succeeded. 769.62/297.03 769.62/297.03 Details of failed attempt(s): 769.62/297.03 ----------------------------- 769.62/297.03 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 769.62/297.03 failed due to the following reason: 769.62/297.03 769.62/297.03 match-boundness of the problem could not be verified. 769.62/297.03 769.62/297.03 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 769.62/297.03 failed due to the following reason: 769.62/297.03 769.62/297.03 match-boundness of the problem could not be verified. 769.62/297.03 769.62/297.03 769.62/297.03 3) 'Best' failed due to the following reason: 769.62/297.03 769.62/297.03 None of the processors succeeded. 769.62/297.03 769.62/297.03 Details of failed attempt(s): 769.62/297.03 ----------------------------- 769.62/297.03 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 769.62/297.03 following reason: 769.62/297.03 769.62/297.03 The processor is inapplicable, reason: 769.62/297.03 Processor only applicable for innermost runtime complexity analysis 769.62/297.03 769.62/297.03 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 769.62/297.03 to the following reason: 769.62/297.03 769.62/297.03 The processor is inapplicable, reason: 769.62/297.03 Processor only applicable for innermost runtime complexity analysis 769.62/297.03 769.62/297.03 769.62/297.03 769.62/297.03 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 769.62/297.03 the following reason: 769.62/297.03 769.62/297.03 We add the following weak dependency pairs: 769.62/297.03 769.62/297.03 Strict DPs: 769.62/297.03 { 0^#(#()) -> c_1() 769.62/297.03 , +^#(x, #()) -> c_2(x) 769.62/297.03 , +^#(0(x), 0(y)) -> c_3(0^#(+(x, y))) 769.62/297.03 , +^#(0(x), 1(y)) -> c_4(+^#(x, y)) 769.62/297.03 , +^#(#(), x) -> c_5(x) 769.62/297.03 , +^#(+(x, y), z) -> c_6(+^#(x, +(y, z))) 769.62/297.03 , +^#(1(x), 0(y)) -> c_7(+^#(x, y)) 769.62/297.03 , +^#(1(x), 1(y)) -> c_8(0^#(+(+(x, y), 1(#())))) 769.62/297.03 , *^#(0(x), y) -> c_9(0^#(*(x, y))) 769.62/297.03 , *^#(#(), x) -> c_10() 769.62/297.03 , *^#(1(x), y) -> c_11(+^#(0(*(x, y)), y)) 769.62/297.03 , *^#(*(x, y), z) -> c_12(*^#(x, *(y, z))) 769.62/297.03 , sum^#(nil()) -> c_13(0^#(#())) 769.62/297.03 , sum^#(cons(x, l)) -> c_14(+^#(x, sum(l))) 769.62/297.03 , prod^#(nil()) -> c_15() 769.62/297.03 , prod^#(cons(x, l)) -> c_16(*^#(x, prod(l))) } 769.62/297.03 769.62/297.03 and mark the set of starting terms. 769.62/297.03 769.62/297.03 We are left with following problem, upon which TcT provides the 769.62/297.03 certificate MAYBE. 769.62/297.03 769.62/297.03 Strict DPs: 769.62/297.03 { 0^#(#()) -> c_1() 769.62/297.03 , +^#(x, #()) -> c_2(x) 769.62/297.03 , +^#(0(x), 0(y)) -> c_3(0^#(+(x, y))) 769.62/297.03 , +^#(0(x), 1(y)) -> c_4(+^#(x, y)) 769.62/297.03 , +^#(#(), x) -> c_5(x) 769.62/297.03 , +^#(+(x, y), z) -> c_6(+^#(x, +(y, z))) 769.62/297.03 , +^#(1(x), 0(y)) -> c_7(+^#(x, y)) 769.62/297.03 , +^#(1(x), 1(y)) -> c_8(0^#(+(+(x, y), 1(#())))) 769.62/297.03 , *^#(0(x), y) -> c_9(0^#(*(x, y))) 769.62/297.03 , *^#(#(), x) -> c_10() 769.62/297.03 , *^#(1(x), y) -> c_11(+^#(0(*(x, y)), y)) 769.62/297.03 , *^#(*(x, y), z) -> c_12(*^#(x, *(y, z))) 769.62/297.03 , sum^#(nil()) -> c_13(0^#(#())) 769.62/297.03 , sum^#(cons(x, l)) -> c_14(+^#(x, sum(l))) 769.62/297.03 , prod^#(nil()) -> c_15() 769.62/297.03 , prod^#(cons(x, l)) -> c_16(*^#(x, prod(l))) } 769.62/297.03 Strict Trs: 769.62/297.03 { 0(#()) -> #() 769.62/297.03 , +(x, #()) -> x 769.62/297.03 , +(0(x), 0(y)) -> 0(+(x, y)) 769.62/297.03 , +(0(x), 1(y)) -> 1(+(x, y)) 769.62/297.03 , +(#(), x) -> x 769.62/297.03 , +(+(x, y), z) -> +(x, +(y, z)) 769.62/297.03 , +(1(x), 0(y)) -> 1(+(x, y)) 769.62/297.03 , +(1(x), 1(y)) -> 0(+(+(x, y), 1(#()))) 769.62/297.03 , *(0(x), y) -> 0(*(x, y)) 769.62/297.03 , *(#(), x) -> #() 769.62/297.03 , *(1(x), y) -> +(0(*(x, y)), y) 769.62/297.03 , *(*(x, y), z) -> *(x, *(y, z)) 769.62/297.03 , sum(nil()) -> 0(#()) 769.62/297.03 , sum(cons(x, l)) -> +(x, sum(l)) 769.62/297.03 , prod(nil()) -> 1(#()) 769.62/297.03 , prod(cons(x, l)) -> *(x, prod(l)) } 769.62/297.03 Obligation: 769.62/297.03 runtime complexity 769.62/297.03 Answer: 769.62/297.03 MAYBE 769.62/297.03 769.62/297.03 We estimate the number of application of {1,10,15} by applications 769.62/297.03 of Pre({1,10,15}) = {2,3,5,8,9,12,13,16}. Here rules are labeled as 769.62/297.03 follows: 769.62/297.03 769.62/297.03 DPs: 769.62/297.03 { 1: 0^#(#()) -> c_1() 769.62/297.03 , 2: +^#(x, #()) -> c_2(x) 769.62/297.03 , 3: +^#(0(x), 0(y)) -> c_3(0^#(+(x, y))) 769.62/297.03 , 4: +^#(0(x), 1(y)) -> c_4(+^#(x, y)) 769.62/297.03 , 5: +^#(#(), x) -> c_5(x) 769.62/297.03 , 6: +^#(+(x, y), z) -> c_6(+^#(x, +(y, z))) 769.62/297.03 , 7: +^#(1(x), 0(y)) -> c_7(+^#(x, y)) 769.62/297.03 , 8: +^#(1(x), 1(y)) -> c_8(0^#(+(+(x, y), 1(#())))) 769.62/297.03 , 9: *^#(0(x), y) -> c_9(0^#(*(x, y))) 769.62/297.03 , 10: *^#(#(), x) -> c_10() 769.62/297.03 , 11: *^#(1(x), y) -> c_11(+^#(0(*(x, y)), y)) 769.62/297.03 , 12: *^#(*(x, y), z) -> c_12(*^#(x, *(y, z))) 769.62/297.03 , 13: sum^#(nil()) -> c_13(0^#(#())) 769.62/297.03 , 14: sum^#(cons(x, l)) -> c_14(+^#(x, sum(l))) 769.62/297.03 , 15: prod^#(nil()) -> c_15() 769.62/297.03 , 16: prod^#(cons(x, l)) -> c_16(*^#(x, prod(l))) } 769.62/297.03 769.62/297.03 We are left with following problem, upon which TcT provides the 769.62/297.03 certificate MAYBE. 769.62/297.03 769.62/297.03 Strict DPs: 769.62/297.03 { +^#(x, #()) -> c_2(x) 769.62/297.03 , +^#(0(x), 0(y)) -> c_3(0^#(+(x, y))) 769.62/297.03 , +^#(0(x), 1(y)) -> c_4(+^#(x, y)) 769.62/297.03 , +^#(#(), x) -> c_5(x) 769.62/297.03 , +^#(+(x, y), z) -> c_6(+^#(x, +(y, z))) 769.62/297.03 , +^#(1(x), 0(y)) -> c_7(+^#(x, y)) 769.62/297.03 , +^#(1(x), 1(y)) -> c_8(0^#(+(+(x, y), 1(#())))) 769.62/297.03 , *^#(0(x), y) -> c_9(0^#(*(x, y))) 769.62/297.03 , *^#(1(x), y) -> c_11(+^#(0(*(x, y)), y)) 769.62/297.03 , *^#(*(x, y), z) -> c_12(*^#(x, *(y, z))) 769.62/297.03 , sum^#(nil()) -> c_13(0^#(#())) 769.62/297.03 , sum^#(cons(x, l)) -> c_14(+^#(x, sum(l))) 769.62/297.03 , prod^#(cons(x, l)) -> c_16(*^#(x, prod(l))) } 769.62/297.03 Strict Trs: 769.62/297.03 { 0(#()) -> #() 769.62/297.03 , +(x, #()) -> x 769.62/297.03 , +(0(x), 0(y)) -> 0(+(x, y)) 769.62/297.03 , +(0(x), 1(y)) -> 1(+(x, y)) 769.62/297.03 , +(#(), x) -> x 769.62/297.03 , +(+(x, y), z) -> +(x, +(y, z)) 769.62/297.03 , +(1(x), 0(y)) -> 1(+(x, y)) 769.62/297.03 , +(1(x), 1(y)) -> 0(+(+(x, y), 1(#()))) 769.62/297.03 , *(0(x), y) -> 0(*(x, y)) 769.62/297.03 , *(#(), x) -> #() 769.62/297.03 , *(1(x), y) -> +(0(*(x, y)), y) 769.62/297.03 , *(*(x, y), z) -> *(x, *(y, z)) 769.62/297.03 , sum(nil()) -> 0(#()) 769.62/297.03 , sum(cons(x, l)) -> +(x, sum(l)) 769.62/297.03 , prod(nil()) -> 1(#()) 769.62/297.03 , prod(cons(x, l)) -> *(x, prod(l)) } 769.62/297.03 Weak DPs: 769.62/297.03 { 0^#(#()) -> c_1() 769.62/297.03 , *^#(#(), x) -> c_10() 769.62/297.03 , prod^#(nil()) -> c_15() } 769.62/297.03 Obligation: 769.62/297.03 runtime complexity 769.62/297.03 Answer: 769.62/297.03 MAYBE 769.62/297.03 769.62/297.03 We estimate the number of application of {2,7,8,11} by applications 769.62/297.03 of Pre({2,7,8,11}) = {1,3,4,5,6,9,10,12,13}. Here rules are labeled 769.62/297.03 as follows: 769.62/297.03 769.62/297.03 DPs: 769.62/297.03 { 1: +^#(x, #()) -> c_2(x) 769.62/297.03 , 2: +^#(0(x), 0(y)) -> c_3(0^#(+(x, y))) 769.62/297.03 , 3: +^#(0(x), 1(y)) -> c_4(+^#(x, y)) 769.62/297.03 , 4: +^#(#(), x) -> c_5(x) 769.62/297.03 , 5: +^#(+(x, y), z) -> c_6(+^#(x, +(y, z))) 769.62/297.03 , 6: +^#(1(x), 0(y)) -> c_7(+^#(x, y)) 769.62/297.03 , 7: +^#(1(x), 1(y)) -> c_8(0^#(+(+(x, y), 1(#())))) 769.62/297.03 , 8: *^#(0(x), y) -> c_9(0^#(*(x, y))) 769.62/297.03 , 9: *^#(1(x), y) -> c_11(+^#(0(*(x, y)), y)) 769.62/297.03 , 10: *^#(*(x, y), z) -> c_12(*^#(x, *(y, z))) 769.62/297.03 , 11: sum^#(nil()) -> c_13(0^#(#())) 769.62/297.03 , 12: sum^#(cons(x, l)) -> c_14(+^#(x, sum(l))) 769.62/297.03 , 13: prod^#(cons(x, l)) -> c_16(*^#(x, prod(l))) 769.62/297.03 , 14: 0^#(#()) -> c_1() 769.62/297.03 , 15: *^#(#(), x) -> c_10() 769.62/297.03 , 16: prod^#(nil()) -> c_15() } 769.62/297.03 769.62/297.03 We are left with following problem, upon which TcT provides the 769.62/297.03 certificate MAYBE. 769.62/297.03 769.62/297.03 Strict DPs: 769.62/297.03 { +^#(x, #()) -> c_2(x) 769.62/297.03 , +^#(0(x), 1(y)) -> c_4(+^#(x, y)) 769.62/297.03 , +^#(#(), x) -> c_5(x) 769.62/297.03 , +^#(+(x, y), z) -> c_6(+^#(x, +(y, z))) 769.62/297.03 , +^#(1(x), 0(y)) -> c_7(+^#(x, y)) 769.62/297.03 , *^#(1(x), y) -> c_11(+^#(0(*(x, y)), y)) 769.62/297.03 , *^#(*(x, y), z) -> c_12(*^#(x, *(y, z))) 769.62/297.03 , sum^#(cons(x, l)) -> c_14(+^#(x, sum(l))) 769.62/297.03 , prod^#(cons(x, l)) -> c_16(*^#(x, prod(l))) } 769.62/297.03 Strict Trs: 769.62/297.03 { 0(#()) -> #() 769.62/297.03 , +(x, #()) -> x 769.62/297.03 , +(0(x), 0(y)) -> 0(+(x, y)) 769.62/297.03 , +(0(x), 1(y)) -> 1(+(x, y)) 769.62/297.03 , +(#(), x) -> x 769.62/297.03 , +(+(x, y), z) -> +(x, +(y, z)) 769.62/297.03 , +(1(x), 0(y)) -> 1(+(x, y)) 769.62/297.03 , +(1(x), 1(y)) -> 0(+(+(x, y), 1(#()))) 769.62/297.03 , *(0(x), y) -> 0(*(x, y)) 769.62/297.03 , *(#(), x) -> #() 769.62/297.03 , *(1(x), y) -> +(0(*(x, y)), y) 769.62/297.03 , *(*(x, y), z) -> *(x, *(y, z)) 769.62/297.03 , sum(nil()) -> 0(#()) 769.62/297.03 , sum(cons(x, l)) -> +(x, sum(l)) 769.62/297.03 , prod(nil()) -> 1(#()) 769.62/297.03 , prod(cons(x, l)) -> *(x, prod(l)) } 769.62/297.03 Weak DPs: 769.62/297.03 { 0^#(#()) -> c_1() 769.62/297.03 , +^#(0(x), 0(y)) -> c_3(0^#(+(x, y))) 769.62/297.03 , +^#(1(x), 1(y)) -> c_8(0^#(+(+(x, y), 1(#())))) 769.62/297.03 , *^#(0(x), y) -> c_9(0^#(*(x, y))) 769.62/297.03 , *^#(#(), x) -> c_10() 769.62/297.03 , sum^#(nil()) -> c_13(0^#(#())) 769.62/297.03 , prod^#(nil()) -> c_15() } 769.62/297.03 Obligation: 769.62/297.03 runtime complexity 769.62/297.03 Answer: 769.62/297.03 MAYBE 769.62/297.03 769.62/297.03 Empty strict component of the problem is NOT empty. 769.62/297.03 769.62/297.03 769.62/297.03 Arrrr.. 769.84/297.27 EOF