/export/starexec/sandbox2/solver/bin/starexec_run_Default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/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,cons(Y,Z))) -> rcons(posrecip(mark(Y)),a__2ndsneg(mark(N),mark(Z))) 4: a__2ndsneg(0(),Z) -> rnil() 5: a__2ndsneg(s(N),cons(X,cons(Y,Z))) -> rcons(negrecip(mark(Y)),a__2ndspos(mark(N),mark(Z))) 6: a__pi(X) -> a__2ndspos(mark(X),a__from(0())) 7: a__plus(0(),Y) -> mark(Y) 8: a__plus(s(X),Y) -> s(a__plus(mark(X),mark(Y))) 9: a__times(0(),Y) -> 0() 10: a__times(s(X),Y) -> a__plus(mark(Y),a__times(mark(X),mark(Y))) 11: a__square(X) -> a__times(mark(X),mark(X)) 12: mark(from(X)) -> a__from(mark(X)) 13: mark(2ndspos(X1,X2)) -> a__2ndspos(mark(X1),mark(X2)) 14: mark(2ndsneg(X1,X2)) -> a__2ndsneg(mark(X1),mark(X2)) 15: mark(pi(X)) -> a__pi(mark(X)) 16: mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2)) 17: mark(times(X1,X2)) -> a__times(mark(X1),mark(X2)) 18: mark(square(X)) -> a__square(mark(X)) 19: mark(0()) -> 0() 20: mark(s(X)) -> s(mark(X)) 21: mark(posrecip(X)) -> posrecip(mark(X)) 22: mark(negrecip(X)) -> negrecip(mark(X)) 23: mark(nil()) -> nil() 24: mark(cons(X1,X2)) -> cons(mark(X1),X2) 25: mark(rnil()) -> rnil() 26: mark(rcons(X1,X2)) -> rcons(mark(X1),mark(X2)) 27: a__from(X) -> from(X) 28: a__2ndspos(X1,X2) -> 2ndspos(X1,X2) 29: a__2ndsneg(X1,X2) -> 2ndsneg(X1,X2) 30: a__pi(X) -> pi(X) 31: a__plus(X1,X2) -> plus(X1,X2) 32: a__times(X1,X2) -> times(X1,X2) 33: a__square(X) -> square(X) Number of strict rules: 33 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #a__pi(X) -> #a__2ndspos(mark(X),a__from(0())) #2: #a__pi(X) -> #mark(X) #3: #a__pi(X) -> #a__from(0()) #4: #mark(2ndspos(X1,X2)) -> #a__2ndspos(mark(X1),mark(X2)) #5: #mark(2ndspos(X1,X2)) -> #mark(X1) #6: #mark(2ndspos(X1,X2)) -> #mark(X2) #7: #a__square(X) -> #a__times(mark(X),mark(X)) #8: #a__square(X) -> #mark(X) #9: #a__square(X) -> #mark(X) #10: #mark(cons(X1,X2)) -> #mark(X1) #11: #mark(from(X)) -> #a__from(mark(X)) #12: #mark(from(X)) -> #mark(X) #13: #mark(2ndsneg(X1,X2)) -> #a__2ndsneg(mark(X1),mark(X2)) #14: #mark(2ndsneg(X1,X2)) -> #mark(X1) #15: #mark(2ndsneg(X1,X2)) -> #mark(X2) #16: #mark(s(X)) -> #mark(X) #17: #a__plus(0(),Y) -> #mark(Y) #18: #a__times(s(X),Y) -> #a__plus(mark(Y),a__times(mark(X),mark(Y))) #19: #a__times(s(X),Y) -> #mark(Y) #20: #a__times(s(X),Y) -> #a__times(mark(X),mark(Y)) #21: #a__times(s(X),Y) -> #mark(X) #22: #a__times(s(X),Y) -> #mark(Y) #23: #a__2ndsneg(s(N),cons(X,cons(Y,Z))) -> #mark(Y) #24: #a__2ndsneg(s(N),cons(X,cons(Y,Z))) -> #a__2ndspos(mark(N),mark(Z)) #25: #a__2ndsneg(s(N),cons(X,cons(Y,Z))) -> #mark(N) #26: #a__2ndsneg(s(N),cons(X,cons(Y,Z))) -> #mark(Z) #27: #mark(negrecip(X)) -> #mark(X) #28: #mark(times(X1,X2)) -> #a__times(mark(X1),mark(X2)) #29: #mark(times(X1,X2)) -> #mark(X1) #30: #mark(times(X1,X2)) -> #mark(X2) #31: #mark(rcons(X1,X2)) -> #mark(X1) #32: #mark(rcons(X1,X2)) -> #mark(X2) #33: #mark(posrecip(X)) -> #mark(X) #34: #mark(plus(X1,X2)) -> #a__plus(mark(X1),mark(X2)) #35: #mark(plus(X1,X2)) -> #mark(X1) #36: #mark(plus(X1,X2)) -> #mark(X2) #37: #a__2ndspos(s(N),cons(X,cons(Y,Z))) -> #mark(Y) #38: #a__2ndspos(s(N),cons(X,cons(Y,Z))) -> #a__2ndsneg(mark(N),mark(Z)) #39: #a__2ndspos(s(N),cons(X,cons(Y,Z))) -> #mark(N) #40: #a__2ndspos(s(N),cons(X,cons(Y,Z))) -> #mark(Z) #41: #a__from(X) -> #mark(X) #42: #a__plus(s(X),Y) -> #a__plus(mark(X),mark(Y)) #43: #a__plus(s(X),Y) -> #mark(X) #44: #a__plus(s(X),Y) -> #mark(Y) #45: #mark(pi(X)) -> #a__pi(mark(X)) #46: #mark(pi(X)) -> #mark(X) #47: #mark(square(X)) -> #a__square(mark(X)) #48: #mark(square(X)) -> #mark(X) Number of SCCs: 1, DPs: 47 SCC { #2..48 } POLO(Sum)... POLO(max)... succeeded. a__plus w: max(x1 + 1, x2) a__2ndsneg w: max(x1 + 3, x2 + 2) negrecip w: x1 + 1 s w: x1 #a__pi w: x1 + 5 #a__from w: x1 + 2 2ndspos w: max(x1 + 3, x2 + 2) a__from w: x1 + 2 rnil w: 3 square w: x1 + 3 #a__times w: max(x1 + 3, x2 + 2) pi w: x1 + 6 rcons w: max(x1, x2) a__2ndspos w: max(x1 + 3, x2 + 2) #a__2ndsneg w: max(x1 + 2, x2 + 2) #a__plus w: max(x1 + 1, x2 + 1) #mark w: x1 + 1 0 w: 2 from w: x1 + 2 times w: max(x1 + 2, x2 + 1) a__pi w: x1 + 6 nil w: 1 mark w: x1 2ndsneg w: max(x1 + 3, x2 + 2) plus w: max(x1 + 1, x2) a__square w: x1 + 3 cons w: max(x1 + 2, x2) a__times w: max(x1 + 2, x2 + 1) #a__square w: x1 + 4 #a__2ndspos w: max(x1 + 2, x2 + 2) posrecip w: x1 + 4 USABLE RULES: { 1..33 } Removed DPs: #2..15 #19 #21..23 #25..27 #29 #30 #33 #35 #37 #39..41 #45 #46 #48 Number of SCCs: 2, DPs: 14 SCC { #24 #38 } POLO(Sum)... POLO(max)... QLPOS... succeeded. a__plus s: [2,1] p: 5 a__2ndsneg s: [1] p: 2 negrecip s: [] p: 4 s s: [1] p: 4 #a__pi s: [] p: 0 #a__from s: [] p: 0 2ndspos s: [2,1] p: 1 a__from s: [] p: 1 rnil s: [] p: 0 square s: [1] p: 7 #a__times s: [2,1] p: 0 pi s: [1] p: 2 rcons s: [] p: 1 a__2ndspos s: [2,1] p: 1 #a__2ndsneg s: [2,1] p: 5 #a__plus s: [2] p: 0 #mark s: [] p: 0 0 s: [] p: 2 from s: [] p: 1 times s: [1,2] p: 6 a__pi s: [1] p: 2 nil s: [] p: 3 mark s: 1 2ndsneg s: [1] p: 2 plus s: [2,1] p: 5 a__square s: [1] p: 7 cons s: 2 a__times s: [1,2] p: 6 #a__square s: [] p: 0 #a__2ndspos s: [2,1] p: 5 posrecip s: [1] p: 5 USABLE RULES: { 1..33 } Removed DPs: #24 #38 Number of SCCs: 1, DPs: 12 SCC { #16..18 #20 #28 #31 #32 #34 #36 #42..44 } POLO(Sum)... POLO(max)... succeeded. a__plus w: max(x1 + 3, x2) a__2ndsneg w: max(x1 + 2) negrecip w: 1 s w: x1 #a__pi w: 5 #a__from w: 2 2ndspos w: max(x1 + 2) a__from w: x1 + 2 rnil w: 1 square w: x1 + 3 #a__times w: max(x1 + 3, x2 + 4) pi w: x1 + 2 rcons w: max(x1 + 1, x2) a__2ndspos w: max(x1 + 2) #a__2ndsneg w: 0 #a__plus w: max(x1 + 2, x2 + 1) #mark w: x1 + 1 0 w: 4 from w: x1 + 2 times w: max(x1 + 2, x2 + 3) a__pi w: x1 + 2 nil w: 1 mark w: x1 2ndsneg w: max(x1 + 2) plus w: max(x1 + 3, x2) a__square w: x1 + 3 cons w: max(x1 + 1) a__times w: max(x1 + 2, x2 + 3) #a__square w: 4 #a__2ndspos w: 0 posrecip w: 1 USABLE RULES: { 1..33 } Removed DPs: #31 #43 Number of SCCs: 1, DPs: 10 SCC { #16..18 #20 #28 #32 #34 #36 #42 #44 } POLO(Sum)... POLO(max)... QLPOS... succeeded. a__plus s: [2,1] p: 6 a__2ndsneg s: [1] p: 2 negrecip s: [] p: 5 s s: [1] p: 2 #a__pi s: [] p: 0 #a__from s: [] p: 0 2ndspos s: [1] p: 2 a__from s: [] p: 1 rnil s: [] p: 0 square s: [1] p: 8 #a__times s: [1,2] p: 7 pi s: [1] p: 3 rcons s: [2] p: 2 a__2ndspos s: [1] p: 2 #a__2ndsneg s: [1] p: 5 #a__plus s: [2] p: 5 #mark s: [1] p: 5 0 s: [] p: 3 from s: [] p: 1 times s: [1,2] p: 7 a__pi s: [1] p: 3 nil s: [] p: 4 mark s: 1 2ndsneg s: [1] p: 2 plus s: [2,1] p: 6 a__square s: [1] p: 8 cons s: 2 a__times s: [1,2] p: 7 #a__square s: [] p: 0 #a__2ndspos s: [1,2] p: 5 posrecip s: [] p: 2 USABLE RULES: { 1..33 } Removed DPs: #16 #18 #28 #32 #34 #36 Number of SCCs: 2, DPs: 2 SCC { #42 } POLO(Sum)... POLO(max)... QLPOS... succeeded. a__plus s: [2,1] p: 7 a__2ndsneg s: [1] p: 2 negrecip s: [] p: 6 s s: [1] p: 2 #a__pi s: [] p: 0 #a__from s: [] p: 0 2ndspos s: [1] p: 2 a__from s: [] p: 1 rnil s: [] p: 0 square s: [1] p: 9 #a__times s: [1,2] p: 7 pi s: [1] p: 4 rcons s: [2] p: 2 a__2ndspos s: [1] p: 2 #a__2ndsneg s: [1] p: 5 #a__plus s: [2,1] p: 3 #mark s: [1] p: 5 0 s: [] p: 4 from s: [] p: 1 times s: [1,2] p: 8 a__pi s: [1] p: 4 nil s: [] p: 5 mark s: 1 2ndsneg s: [1] p: 2 plus s: [2,1] p: 7 a__square s: [1] p: 9 cons s: 2 a__times s: [1,2] p: 8 #a__square s: [] p: 0 #a__2ndspos s: [1,2] p: 5 posrecip s: [] p: 2 USABLE RULES: { 1..33 } Removed DPs: #42 Number of SCCs: 1, DPs: 1 SCC { #20 } POLO(Sum)... POLO(max)... QLPOS... succeeded. a__plus s: [2,1] p: 7 a__2ndsneg s: [1] p: 2 negrecip s: [] p: 6 s s: [1] p: 2 #a__pi s: [] p: 0 #a__from s: [] p: 0 2ndspos s: [1] p: 2 a__from s: [] p: 1 rnil s: [] p: 0 square s: [1] p: 9 #a__times s: [1,2] p: 3 pi s: [1] p: 4 rcons s: [2] p: 2 a__2ndspos s: [1] p: 2 #a__2ndsneg s: [1] p: 5 #a__plus s: [2,1] p: 3 #mark s: [1] p: 5 0 s: [] p: 4 from s: [] p: 1 times s: [1,2] p: 8 a__pi s: [1] p: 4 nil s: [] p: 5 mark s: 1 2ndsneg s: [1] p: 2 plus s: [2,1] p: 7 a__square s: [1] p: 9 cons s: 2 a__times s: [1,2] p: 8 #a__square s: [] p: 0 #a__2ndspos s: [1,2] p: 5 posrecip s: [] p: 2 USABLE RULES: { 1..33 } Removed DPs: #20 Number of SCCs: 0, DPs: 0