/export/starexec/sandbox/solver/bin/starexec_run_Default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Input TRS: 1: a__from(X) -> cons(mark(X),from(s(X))) 2: a__2ndspos(0(),Z) -> rnil() 3: a__2ndspos(s(N),cons(X,Z)) -> a__2ndspos(s(mark(N)),cons2(X,mark(Z))) 4: a__2ndspos(s(N),cons2(X,cons(Y,Z))) -> rcons(posrecip(mark(Y)),a__2ndsneg(mark(N),mark(Z))) 5: a__2ndsneg(0(),Z) -> rnil() 6: a__2ndsneg(s(N),cons(X,Z)) -> a__2ndsneg(s(mark(N)),cons2(X,mark(Z))) 7: a__2ndsneg(s(N),cons2(X,cons(Y,Z))) -> rcons(negrecip(mark(Y)),a__2ndspos(mark(N),mark(Z))) 8: a__pi(X) -> a__2ndspos(mark(X),a__from(0())) 9: a__plus(0(),Y) -> mark(Y) 10: a__plus(s(X),Y) -> s(a__plus(mark(X),mark(Y))) 11: a__times(0(),Y) -> 0() 12: a__times(s(X),Y) -> a__plus(mark(Y),a__times(mark(X),mark(Y))) 13: a__square(X) -> a__times(mark(X),mark(X)) 14: mark(from(X)) -> a__from(mark(X)) 15: mark(2ndspos(X1,X2)) -> a__2ndspos(mark(X1),mark(X2)) 16: mark(2ndsneg(X1,X2)) -> a__2ndsneg(mark(X1),mark(X2)) 17: mark(pi(X)) -> a__pi(mark(X)) 18: mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2)) 19: mark(times(X1,X2)) -> a__times(mark(X1),mark(X2)) 20: mark(square(X)) -> a__square(mark(X)) 21: mark(0()) -> 0() 22: mark(s(X)) -> s(mark(X)) 23: mark(posrecip(X)) -> posrecip(mark(X)) 24: mark(negrecip(X)) -> negrecip(mark(X)) 25: mark(nil()) -> nil() 26: mark(cons(X1,X2)) -> cons(mark(X1),X2) 27: mark(cons2(X1,X2)) -> cons2(X1,mark(X2)) 28: mark(rnil()) -> rnil() 29: mark(rcons(X1,X2)) -> rcons(mark(X1),mark(X2)) 30: a__from(X) -> from(X) 31: a__2ndspos(X1,X2) -> 2ndspos(X1,X2) 32: a__2ndsneg(X1,X2) -> 2ndsneg(X1,X2) 33: a__pi(X) -> pi(X) 34: a__plus(X1,X2) -> plus(X1,X2) 35: a__times(X1,X2) -> times(X1,X2) 36: a__square(X) -> square(X) Number of strict rules: 36 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #mark(rcons(X1,X2)) -> #mark(X1) #2: #mark(rcons(X1,X2)) -> #mark(X2) #3: #a__2ndsneg(s(N),cons(X,Z)) -> #a__2ndsneg(s(mark(N)),cons2(X,mark(Z))) #4: #a__2ndsneg(s(N),cons(X,Z)) -> #mark(N) #5: #a__2ndsneg(s(N),cons(X,Z)) -> #mark(Z) #6: #a__square(X) -> #a__times(mark(X),mark(X)) #7: #a__square(X) -> #mark(X) #8: #a__square(X) -> #mark(X) #9: #a__plus(0(),Y) -> #mark(Y) #10: #mark(negrecip(X)) -> #mark(X) #11: #mark(posrecip(X)) -> #mark(X) #12: #a__times(s(X),Y) -> #a__plus(mark(Y),a__times(mark(X),mark(Y))) #13: #a__times(s(X),Y) -> #mark(Y) #14: #a__times(s(X),Y) -> #a__times(mark(X),mark(Y)) #15: #a__times(s(X),Y) -> #mark(X) #16: #a__times(s(X),Y) -> #mark(Y) #17: #mark(from(X)) -> #a__from(mark(X)) #18: #mark(from(X)) -> #mark(X) #19: #mark(square(X)) -> #a__square(mark(X)) #20: #mark(square(X)) -> #mark(X) #21: #a__2ndsneg(s(N),cons2(X,cons(Y,Z))) -> #mark(Y) #22: #a__2ndsneg(s(N),cons2(X,cons(Y,Z))) -> #a__2ndspos(mark(N),mark(Z)) #23: #a__2ndsneg(s(N),cons2(X,cons(Y,Z))) -> #mark(N) #24: #a__2ndsneg(s(N),cons2(X,cons(Y,Z))) -> #mark(Z) #25: #a__plus(s(X),Y) -> #a__plus(mark(X),mark(Y)) #26: #a__plus(s(X),Y) -> #mark(X) #27: #a__plus(s(X),Y) -> #mark(Y) #28: #mark(s(X)) -> #mark(X) #29: #mark(cons2(X1,X2)) -> #mark(X2) #30: #mark(pi(X)) -> #a__pi(mark(X)) #31: #mark(pi(X)) -> #mark(X) #32: #mark(times(X1,X2)) -> #a__times(mark(X1),mark(X2)) #33: #mark(times(X1,X2)) -> #mark(X1) #34: #mark(times(X1,X2)) -> #mark(X2) #35: #mark(cons(X1,X2)) -> #mark(X1) #36: #mark(2ndsneg(X1,X2)) -> #a__2ndsneg(mark(X1),mark(X2)) #37: #mark(2ndsneg(X1,X2)) -> #mark(X1) #38: #mark(2ndsneg(X1,X2)) -> #mark(X2) #39: #a__2ndspos(s(N),cons(X,Z)) -> #a__2ndspos(s(mark(N)),cons2(X,mark(Z))) #40: #a__2ndspos(s(N),cons(X,Z)) -> #mark(N) #41: #a__2ndspos(s(N),cons(X,Z)) -> #mark(Z) #42: #a__from(X) -> #mark(X) #43: #a__pi(X) -> #a__2ndspos(mark(X),a__from(0())) #44: #a__pi(X) -> #mark(X) #45: #a__pi(X) -> #a__from(0()) #46: #mark(2ndspos(X1,X2)) -> #a__2ndspos(mark(X1),mark(X2)) #47: #mark(2ndspos(X1,X2)) -> #mark(X1) #48: #mark(2ndspos(X1,X2)) -> #mark(X2) #49: #a__2ndspos(s(N),cons2(X,cons(Y,Z))) -> #mark(Y) #50: #a__2ndspos(s(N),cons2(X,cons(Y,Z))) -> #a__2ndsneg(mark(N),mark(Z)) #51: #a__2ndspos(s(N),cons2(X,cons(Y,Z))) -> #mark(N) #52: #a__2ndspos(s(N),cons2(X,cons(Y,Z))) -> #mark(Z) #53: #mark(plus(X1,X2)) -> #a__plus(mark(X1),mark(X2)) #54: #mark(plus(X1,X2)) -> #mark(X1) #55: #mark(plus(X1,X2)) -> #mark(X2) Number of SCCs: 1, DPs: 55 SCC { #1..55 } POLO(Sum)... POLO(max)... succeeded. a__plus w: max(x1 + 2, x2) a__2ndsneg w: max(x1 + 2, x2 + 3) negrecip w: x1 + 3 s w: x1 #a__pi w: x1 + 8 #a__from w: x1 + 2 2ndspos w: max(x1 + 2, x2 + 3) a__from w: x1 + 2 rnil w: 4 square w: x1 + 5 #a__times w: max(x1 + 4, x2 + 3) pi w: x1 + 8 rcons w: max(x1 + 1, x2) a__2ndspos w: max(x1 + 2, x2 + 3) #a__2ndsneg w: max(x1 + 3, x2 + 2) #a__plus w: max(x1 + 2, x2 + 1) #mark w: x1 + 1 0 w: 3 from w: x1 + 2 times w: max(x1 + 3, x2 + 2) a__pi w: x1 + 8 nil w: 1 mark w: x1 2ndsneg w: max(x1 + 2, x2 + 3) plus w: max(x1 + 2, x2) cons2 w: max(x2) a__square w: x1 + 5 cons w: max(x1 + 2, x2) a__times w: max(x1 + 3, x2 + 2) #a__square w: x1 + 5 #a__2ndspos w: max(x1 + 3, x2 + 2) posrecip w: x1 + 3 USABLE RULES: { 1..36 } Removed DPs: #1 #4..8 #10 #11 #13 #15..21 #23 #24 #26 #30 #31 #33..35 #37 #38 #40..45 #47..49 #51 #52 #54 Number of SCCs: 2, DPs: 15 SCC { #3 #22 #39 #50 } POLO(Sum)... POLO(max)... QLPOS... succeeded. a__plus s: [2,1] p: 3 a__2ndsneg s: 1 negrecip s: [] p: 3 s s: [1] p: 2 #a__pi s: [] p: 0 #a__from s: [] p: 0 2ndspos s: 1 a__from s: [1] p: 3 rnil s: [] p: 5 square s: [1] p: 6 #a__times s: [2] p: 0 pi s: 1 rcons s: 2 a__2ndspos s: 1 #a__2ndsneg s: 1 #a__plus s: [1,2] p: 0 #mark s: [] p: 0 0 s: [] p: 5 from s: [1] p: 3 times s: [2,1] p: 5 a__pi s: 1 nil s: [] p: 2 mark s: 1 2ndsneg s: 1 plus s: [2,1] p: 3 cons2 s: 1 a__square s: [1] p: 6 cons s: [1] p: 3 a__times s: [2,1] p: 5 #a__square s: [] p: 0 #a__2ndspos s: 1 posrecip s: [] p: 3 USABLE RULES: { 1..36 } Removed DPs: #22 #50 Number of SCCs: 1, DPs: 11 SCC { #2 #9 #12 #14 #25 #27..29 #32 #53 #55 } POLO(Sum)... succeeded. a__plus w: x2 a__2ndsneg w: 1 negrecip w: 1 s w: x1 #a__pi w: 2 #a__from w: 2 2ndspos w: 1 a__from w: 1 rnil w: 1 square w: x1 + 1 #a__times w: x2 + 1 pi w: 1 rcons w: x2 a__2ndspos w: 1 #a__2ndsneg w: 0 #a__plus w: x2 #mark w: x1 0 w: 1 from w: 1 times w: x2 + 1 a__pi w: 1 nil w: 1 mark w: x1 2ndsneg w: 1 plus w: x2 cons2 w: x2 + 1 a__square w: x1 + 1 cons w: 1 a__times w: x2 + 1 #a__square w: 2 #a__2ndspos w: 0 posrecip w: 1 USABLE RULES: { 1..36 } Removed DPs: #29 Number of SCCs: 1, DPs: 10 SCC { #2 #9 #12 #14 #25 #27 #28 #32 #53 #55 } POLO(Sum)... POLO(max)... QLPOS... succeeded. a__plus s: [2,1] p: 5 a__2ndsneg s: 1 negrecip s: [] p: 3 s s: [1] p: 2 #a__pi s: [] p: 0 #a__from s: [] p: 0 2ndspos s: 1 a__from s: [1] p: 3 rnil s: [] p: 7 square s: [1] p: 8 #a__times s: [2,1] p: 7 pi s: 1 rcons s: [2] p: 0 a__2ndspos s: 1 #a__2ndsneg s: 1 #a__plus s: [1,2] p: 4 #mark s: [1] p: 3 0 s: [] p: 7 from s: [1] p: 3 times s: [2,1] p: 7 a__pi s: 1 nil s: [] p: 2 mark s: 1 2ndsneg s: 1 plus s: [2,1] p: 5 cons2 s: 1 a__square s: [1] p: 8 cons s: [1] p: 3 a__times s: [2,1] p: 7 #a__square s: [] p: 0 #a__2ndspos s: 1 posrecip s: [] p: 3 USABLE RULES: { 1..36 } Removed DPs: #2 #9 #12 #14 #25 #27 #28 #32 #53 #55 Number of SCCs: 0, DPs: 0