/export/starexec/sandbox2/solver/bin/starexec_run_Default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Input TRS: 1: -(x,0()) -> x 2: -(s(x),s(y)) -> -(x,y) 3: *(x,0()) -> 0() 4: *(x,s(y)) -> +(*(x,y),x) 5: if(true(),x,y) -> x 6: if(false(),x,y) -> y 7: odd(0()) -> false() 8: odd(s(0())) -> true() 9: odd(s(s(x))) -> odd(x) 10: half(0()) -> 0() 11: half(s(0())) -> 0() 12: half(s(s(x))) -> s(half(x)) 13: if(true(),x,y) -> true() 14: if(false(),x,y) -> false() 15: pow(x,y) -> f(x,y,s(0())) 16: f(x,0(),z) -> z 17: f(x,s(y),z) -> if(odd(s(y)),f(x,y,*(x,z)),f(*(x,x),half(s(y)),z)) Number of strict rules: 17 Direct POLO(bPol) ... failed. Uncurrying half odd 1: -(x,0()) -> x 2: -(s(x),s(y)) -> -(x,y) 3: *(x,0()) -> 0() 4: *(x,s(y)) -> +(*(x,y),x) 5: if(true(),x,y) -> x 6: if(false(),x,y) -> y 7: odd^1_0() -> false() 8: odd^1_s(0()) -> true() 9: odd^1_s(s(x)) -> odd(x) 10: half^1_0() -> 0() 11: half^1_s(0()) -> 0() 12: half^1_s(s(x)) -> s(half(x)) 13: if(true(),x,y) -> true() 14: if(false(),x,y) -> false() 15: pow(x,y) -> f(x,y,s(0())) 16: f(x,0(),z) -> z 17: f(x,s(y),z) -> if(odd^1_s(y),f(x,y,*(x,z)),f(*(x,x),half^1_s(y),z)) 18: odd(0()) ->= odd^1_0() 19: odd(s(_1)) ->= odd^1_s(_1) 20: half(0()) ->= half^1_0() 21: half(s(_1)) ->= half^1_s(_1) Number of strict rules: 17 Direct POLO(bPol) ... failed. Dependency Pairs: #1: #-(s(x),s(y)) -> #-(x,y) #2: #odd^1_s(s(x)) -> #odd(x) #3: #half^1_s(s(x)) -> #half(x) #4: #half(0()) ->? #half^1_0() #5: #f(x,s(y),z) -> #if(odd^1_s(y),f(x,y,*(x,z)),f(*(x,x),half^1_s(y),z)) #6: #f(x,s(y),z) -> #odd^1_s(y) #7: #f(x,s(y),z) -> #f(x,y,*(x,z)) #8: #f(x,s(y),z) -> #*(x,z) #9: #f(x,s(y),z) -> #f(*(x,x),half^1_s(y),z) #10: #f(x,s(y),z) -> #*(x,x) #11: #f(x,s(y),z) -> #half^1_s(y) #12: #odd(s(_1)) ->? #odd^1_s(_1) #13: #half(s(_1)) ->? #half^1_s(_1) #14: #pow(x,y) -> #f(x,y,s(0())) #15: #*(x,s(y)) -> #*(x,y) #16: #odd(0()) ->? #odd^1_0() Number of SCCs: 5, DPs: 8 SCC { #15 } POLO(Sum)... succeeded. s w: x1 + 1 pow w: 0 false w: 0 #* w: x2 #half w: 0 #odd^1_0 w: 0 half^1_s w: 0 true w: 0 #pow w: 0 f w: 0 half w: 0 odd^1_0 w: 0 0 w: 0 if w: 0 #half^1_s w: 0 - w: 0 #f w: 0 odd^1_s w: 0 #odd^1_s w: 0 #odd w: 0 half^1_0 w: 0 odd w: 0 #- w: 0 #if w: 0 #half^1_0 w: 0 + w: 0 * w: 0 USABLE RULES: { } Removed DPs: #15 Number of SCCs: 4, DPs: 7 SCC { #1 } POLO(Sum)... succeeded. s w: x1 + 1 pow w: 0 false w: 0 #* w: 0 #half w: 0 #odd^1_0 w: 0 half^1_s w: 0 true w: 0 #pow w: 0 f w: 0 half w: 0 odd^1_0 w: 0 0 w: 0 if w: 0 #half^1_s w: 0 - w: 0 #f w: 0 odd^1_s w: 0 #odd^1_s w: 0 #odd w: 0 half^1_0 w: 0 odd w: 0 #- w: x2 #if w: 0 #half^1_0 w: 0 + w: 0 * w: 0 USABLE RULES: { } Removed DPs: #1 Number of SCCs: 3, DPs: 6 SCC { #3 #13 } POLO(Sum)... succeeded. s w: x1 + 1 pow w: 0 false w: 0 #* w: 0 #half w: x1 #odd^1_0 w: 0 half^1_s w: 0 true w: 0 #pow w: 0 f w: 0 half w: 0 odd^1_0 w: 0 0 w: 0 if w: 0 #half^1_s w: x1 - w: 0 #f w: 0 odd^1_s w: 0 #odd^1_s w: 0 #odd w: 0 half^1_0 w: 0 odd w: 0 #- w: 0 #if w: 0 #half^1_0 w: 0 + w: 0 * w: 0 USABLE RULES: { } Removed DPs: #3 #13 Number of SCCs: 2, DPs: 4 SCC { #2 #12 } POLO(Sum)... succeeded. s w: x1 + 1 pow w: 0 false w: 0 #* w: 0 #half w: 0 #odd^1_0 w: 0 half^1_s w: 0 true w: 0 #pow w: 0 f w: 0 half w: 0 odd^1_0 w: 0 0 w: 0 if w: 0 #half^1_s w: 0 - w: 0 #f w: 0 odd^1_s w: 0 #odd^1_s w: x1 #odd w: x1 half^1_0 w: 0 odd w: 0 #- w: 0 #if w: 0 #half^1_0 w: 0 + w: 0 * w: 0 USABLE RULES: { } Removed DPs: #2 #12 Number of SCCs: 1, DPs: 2 SCC { #7 #9 } POLO(Sum)... succeeded. s w: x1 + 2 pow w: 0 false w: 0 #* w: 0 #half w: 0 #odd^1_0 w: 0 half^1_s w: x1 + 1 true w: 0 #pow w: 0 f w: 0 half w: x1 + 1 odd^1_0 w: 0 0 w: 1 if w: 0 #half^1_s w: 0 - w: 0 #f w: x2 odd^1_s w: 0 #odd^1_s w: 0 #odd w: 0 half^1_0 w: 1 odd w: 0 #- w: 0 #if w: 0 #half^1_0 w: 0 + w: x1 * w: x1 + x2 + 1 USABLE RULES: { 10..12 20 21 } Removed DPs: #7 #9 Number of SCCs: 0, DPs: 0