/export/starexec/sandbox2/solver/bin/starexec_run_Default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- MAYBE Input TRS: 1: a(x1) -> x1 2: o(x1) -> x1 3: l(x1) -> x1 4: S(x1) -> x1 5: +(x1,x2) -> x2 6: +(x1,x2) -> x1 7: P(x1,x2,x3,x4) -> x4 8: P(x1,x2,x3,x4) -> x3 9: P(x1,x2,x3,x4) -> x2 10: P(x1,x2,x3,x4) -> x1 11: M(x1,x2,x3,x4) -> x4 12: M(x1,x2,x3,x4) -> x3 13: M(x1,x2,x3,x4) -> x2 14: M(x1,x2,x3,x4) -> x1 15: J1(x1,x2) -> x2 16: J1(x1,x2) -> x1 17: J2(x1,x2,x3) -> x3 18: J2(x1,x2,x3) -> x2 19: J2(x1,x2,x3) -> x1 20: J3(x1,x2,x3,x4) -> x4 21: J3(x1,x2,x3,x4) -> x3 22: J3(x1,x2,x3,x4) -> x2 23: J3(x1,x2,x3,x4) -> x1 24: Q11(x1,x2) -> x2 25: Q11(x1,x2) -> x1 26: Q21(x1,x2,x3) -> x3 27: Q21(x1,x2,x3) -> x2 28: Q21(x1,x2,x3) -> x1 29: Q22(x1,x2,x3) -> x3 30: Q22(x1,x2,x3) -> x2 31: Q22(x1,x2,x3) -> x1 32: Q31(x1,x2,x3,x4) -> x4 33: Q31(x1,x2,x3,x4) -> x3 34: Q31(x1,x2,x3,x4) -> x2 35: Q31(x1,x2,x3,x4) -> x1 36: Q32(x1,x2,x3,x4) -> x4 37: Q32(x1,x2,x3,x4) -> x3 38: Q32(x1,x2,x3,x4) -> x2 39: Q32(x1,x2,x3,x4) -> x1 40: Q33(x1,x2,x3,x4) -> x4 41: Q33(x1,x2,x3,x4) -> x3 42: Q33(x1,x2,x3,x4) -> x2 43: Q33(x1,x2,x3,x4) -> x1 44: R1(x1,x2,x3) -> x3 45: R1(x1,x2,x3) -> x2 46: R1(x1,x2,x3) -> x1 47: R2(x1,x2,x3,x4) -> x4 48: R2(x1,x2,x3,x4) -> x3 49: R2(x1,x2,x3,x4) -> x2 50: R2(x1,x2,x3,x4) -> x1 51: R3(x1,x2,x3,x4,x5) -> x5 52: R3(x1,x2,x3,x4,x5) -> x4 53: R3(x1,x2,x3,x4,x5) -> x3 54: R3(x1,x2,x3,x4,x5) -> x2 55: R3(x1,x2,x3,x4,x5) -> x1 56: P(0(),0(),0(),0()) -> S(0()) 57: +(x,S(y)) -> S(+(x,y)) 58: a(l(x)) -> l(a(a(x))) 59: l(o(x)) -> o(l(l(x))) 60: o(x) -> l(x) 61: l(x) -> a(x) 62: a(S(x)) -> S(l(x)) 63: a(+(x,y)) -> +(l(x),y) 64: a(+(x,y)) -> +(x,l(y)) 65: a(P(x1,x2,x3,x4)) -> P(x1,x2,x3,l(x4)) 66: a(P(x1,x2,x3,x4)) -> P(x1,x2,l(x3),x4) 67: a(P(x1,x2,x3,x4)) -> P(x1,l(x2),x3,x4) 68: a(P(x1,x2,x3,x4)) -> P(l(x1),x2,x3,x4) 69: +(x,o(y)) -> o(+(x,y)) 70: P(x1,x2,x3,o(x4)) -> o(P(x1,x2,x3,x4)) 71: P(x1,x2,o(x3),x4) -> o(P(x1,x2,x3,x4)) 72: P(x1,o(x2),x3,x4) -> o(P(x1,x2,x3,x4)) 73: P(o(x1),x2,x3,x4) -> o(P(x1,x2,x3,x4)) 74: M(x1,x2,x3,l(y)) -> +(M(x1,x2,x3,y),P(x1,x2,x3,y)) 75: J3(x1,x2,l(x3),y) -> P(x1,x2,J3(x1,x2,x3,y),0()) 76: J2(x1,l(x2),y) -> P(x1,J2(x1,x2,y),0(),0()) 77: J1(l(x1),y) -> P(J1(x1,y),0(),0(),0()) 78: a(S(x)) -> o(x) 79: P(0(),0(),0(),S(y)) -> o(M(0(),0(),0(),y)) 80: P(0(),0(),0(),P(x1,x2,x3,y)) -> o(M(x1,x2,x3,y)) 81: P(x1,x2,S(x3),y) -> o(J3(x1,x2,x3,y)) 82: P(x1,S(x2),0(),y) -> o(J2(x1,x2,y)) 83: P(S(x1),0(),0(),y) -> o(J1(x1,y)) 84: P(x1,x2,S(x3),S(y)) -> o(J3(x1,x2,x3,P(x1,x2,S(x3),y))) 85: P(x1,S(x2),0(),S(y)) -> o(J2(x1,x2,P(x1,S(x2),0(),y))) 86: P(S(x1),0(),0(),S(y)) -> o(J1(x1,P(S(x1),0(),0(),y))) 87: a(P(x1,x2,x3,0())) -> Q33(x1,x2,a(x3),x3) 88: a(P(x1,x2,x3,0())) -> Q32(x1,x2,a(x3),x2) 89: a(P(x1,x2,x3,0())) -> Q31(x1,x2,a(x3),x1) 90: a(P(x1,x2,0(),0())) -> Q22(x1,a(x2),x2) 91: a(P(x1,x2,0(),0())) -> Q21(x1,a(x2),x1) 92: a(P(x1,0(),0(),0())) -> Q11(a(x1),x1) 93: Q33(x1,x2,o(x3),y) -> o(P(x1,x2,x3,y)) 94: Q32(x1,x2,o(x3),y) -> o(P(x1,x2,x3,y)) 95: Q31(x1,x2,o(x3),y) -> o(P(x1,x2,x3,y)) 96: Q22(x1,o(x2),y) -> o(P(x1,x2,0(),y)) 97: Q21(x1,o(x2),y) -> o(P(x1,x2,0(),y)) 98: Q11(o(x1),y) -> o(P(x1,0(),0(),y)) 99: a(P(x1,x2,x3,S(y))) -> R3(x1,x2,a(x3),x3,y) 100: a(P(x1,x2,0(),S(y))) -> R2(x1,a(x2),x2,y) 101: a(P(x1,0(),0(),S(y))) -> R1(a(x1),x1,y) 102: R3(x1,x2,o(x3),y,z) -> o(P(x1,x2,x3,P(x1,x2,y,z))) 103: R2(x1,o(x2),y,z) -> o(P(x1,x2,0(),P(x1,y,0(),z))) 104: R1(o(x1),y,z) -> o(P(x1,0(),0(),P(y,0(),0(),z))) Number of strict rules: 104 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #P(S(x1),0(),0(),S(y)) -> #o(J1(x1,P(S(x1),0(),0(),y))) #2: #P(S(x1),0(),0(),S(y)) -> #J1(x1,P(S(x1),0(),0(),y)) #3: #P(S(x1),0(),0(),S(y)) -> #P(S(x1),0(),0(),y) #4: #P(S(x1),0(),0(),y) -> #o(J1(x1,y)) #5: #P(S(x1),0(),0(),y) -> #J1(x1,y) #6: #a(P(x1,x2,x3,x4)) -> #P(x1,x2,l(x3),x4) #7: #a(P(x1,x2,x3,x4)) -> #l(x3) #8: #Q31(x1,x2,o(x3),y) -> #o(P(x1,x2,x3,y)) #9: #Q31(x1,x2,o(x3),y) -> #P(x1,x2,x3,y) #10: #a(P(x1,x2,x3,S(y))) -> #R3(x1,x2,a(x3),x3,y) #11: #a(P(x1,x2,x3,S(y))) -> #a(x3) #12: #Q21(x1,o(x2),y) -> #o(P(x1,x2,0(),y)) #13: #Q21(x1,o(x2),y) -> #P(x1,x2,0(),y) #14: #a(P(x1,x2,0(),0())) -> #Q21(x1,a(x2),x1) #15: #a(P(x1,x2,0(),0())) -> #a(x2) #16: #P(o(x1),x2,x3,x4) -> #o(P(x1,x2,x3,x4)) #17: #P(o(x1),x2,x3,x4) -> #P(x1,x2,x3,x4) #18: #P(x1,x2,o(x3),x4) -> #o(P(x1,x2,x3,x4)) #19: #P(x1,x2,o(x3),x4) -> #P(x1,x2,x3,x4) #20: #J3(x1,x2,l(x3),y) -> #P(x1,x2,J3(x1,x2,x3,y),0()) #21: #J3(x1,x2,l(x3),y) -> #J3(x1,x2,x3,y) #22: #M(x1,x2,x3,l(y)) -> #+(M(x1,x2,x3,y),P(x1,x2,x3,y)) #23: #M(x1,x2,x3,l(y)) -> #M(x1,x2,x3,y) #24: #M(x1,x2,x3,l(y)) -> #P(x1,x2,x3,y) #25: #a(l(x)) -> #l(a(a(x))) #26: #a(l(x)) -> #a(a(x)) #27: #a(l(x)) -> #a(x) #28: #l(x) -> #a(x) #29: #l(o(x)) -> #o(l(l(x))) #30: #l(o(x)) -> #l(l(x)) #31: #l(o(x)) -> #l(x) #32: #a(P(x1,x2,x3,x4)) -> #P(x1,l(x2),x3,x4) #33: #a(P(x1,x2,x3,x4)) -> #l(x2) #34: #a(P(x1,x2,0(),0())) -> #Q22(x1,a(x2),x2) #35: #a(P(x1,x2,0(),0())) -> #a(x2) #36: #Q11(o(x1),y) -> #o(P(x1,0(),0(),y)) #37: #Q11(o(x1),y) -> #P(x1,0(),0(),y) #38: #+(x,S(y)) -> #S(+(x,y)) #39: #+(x,S(y)) -> #+(x,y) #40: #J2(x1,l(x2),y) -> #P(x1,J2(x1,x2,y),0(),0()) #41: #J2(x1,l(x2),y) -> #J2(x1,x2,y) #42: #Q32(x1,x2,o(x3),y) -> #o(P(x1,x2,x3,y)) #43: #Q32(x1,x2,o(x3),y) -> #P(x1,x2,x3,y) #44: #P(x1,x2,x3,o(x4)) -> #o(P(x1,x2,x3,x4)) #45: #P(x1,x2,x3,o(x4)) -> #P(x1,x2,x3,x4) #46: #P(x1,x2,S(x3),y) -> #o(J3(x1,x2,x3,y)) #47: #P(x1,x2,S(x3),y) -> #J3(x1,x2,x3,y) #48: #a(S(x)) -> #o(x) #49: #Q22(x1,o(x2),y) -> #o(P(x1,x2,0(),y)) #50: #Q22(x1,o(x2),y) -> #P(x1,x2,0(),y) #51: #+(x,o(y)) -> #o(+(x,y)) #52: #+(x,o(y)) -> #+(x,y) #53: #a(P(x1,0(),0(),S(y))) -> #R1(a(x1),x1,y) #54: #a(P(x1,0(),0(),S(y))) -> #a(x1) #55: #P(0(),0(),0(),S(y)) -> #o(M(0(),0(),0(),y)) #56: #P(0(),0(),0(),S(y)) -> #M(0(),0(),0(),y) #57: #P(0(),0(),0(),0()) -> #S(0()) #58: #a(P(x1,x2,x3,0())) -> #Q31(x1,x2,a(x3),x1) #59: #a(P(x1,x2,x3,0())) -> #a(x3) #60: #P(x1,S(x2),0(),y) -> #o(J2(x1,x2,y)) #61: #P(x1,S(x2),0(),y) -> #J2(x1,x2,y) #62: #a(S(x)) -> #S(l(x)) #63: #a(S(x)) -> #l(x) #64: #a(P(x1,x2,x3,0())) -> #Q32(x1,x2,a(x3),x2) #65: #a(P(x1,x2,x3,0())) -> #a(x3) #66: #a(P(x1,0(),0(),0())) -> #Q11(a(x1),x1) #67: #a(P(x1,0(),0(),0())) -> #a(x1) #68: #Q33(x1,x2,o(x3),y) -> #o(P(x1,x2,x3,y)) #69: #Q33(x1,x2,o(x3),y) -> #P(x1,x2,x3,y) #70: #a(+(x,y)) -> #+(x,l(y)) #71: #a(+(x,y)) -> #l(y) #72: #P(x1,o(x2),x3,x4) -> #o(P(x1,x2,x3,x4)) #73: #P(x1,o(x2),x3,x4) -> #P(x1,x2,x3,x4) #74: #a(P(x1,x2,x3,x4)) -> #P(x1,x2,x3,l(x4)) #75: #a(P(x1,x2,x3,x4)) -> #l(x4) #76: #P(x1,x2,S(x3),S(y)) -> #o(J3(x1,x2,x3,P(x1,x2,S(x3),y))) #77: #P(x1,x2,S(x3),S(y)) -> #J3(x1,x2,x3,P(x1,x2,S(x3),y)) #78: #P(x1,x2,S(x3),S(y)) -> #P(x1,x2,S(x3),y) #79: #a(P(x1,x2,x3,0())) -> #Q33(x1,x2,a(x3),x3) #80: #a(P(x1,x2,x3,0())) -> #a(x3) #81: #o(x) -> #l(x) #82: #a(+(x,y)) -> #+(l(x),y) #83: #a(+(x,y)) -> #l(x) #84: #a(P(x1,x2,0(),S(y))) -> #R2(x1,a(x2),x2,y) #85: #a(P(x1,x2,0(),S(y))) -> #a(x2) #86: #P(x1,S(x2),0(),S(y)) -> #o(J2(x1,x2,P(x1,S(x2),0(),y))) #87: #P(x1,S(x2),0(),S(y)) -> #J2(x1,x2,P(x1,S(x2),0(),y)) #88: #P(x1,S(x2),0(),S(y)) -> #P(x1,S(x2),0(),y) #89: #a(P(x1,x2,x3,x4)) -> #P(l(x1),x2,x3,x4) #90: #a(P(x1,x2,x3,x4)) -> #l(x1) #91: #J1(l(x1),y) -> #P(J1(x1,y),0(),0(),0()) #92: #J1(l(x1),y) -> #J1(x1,y) #93: #R3(x1,x2,o(x3),y,z) -> #o(P(x1,x2,x3,P(x1,x2,y,z))) #94: #R3(x1,x2,o(x3),y,z) -> #P(x1,x2,x3,P(x1,x2,y,z)) #95: #R3(x1,x2,o(x3),y,z) -> #P(x1,x2,y,z) #96: #R2(x1,o(x2),y,z) -> #o(P(x1,x2,0(),P(x1,y,0(),z))) #97: #R2(x1,o(x2),y,z) -> #P(x1,x2,0(),P(x1,y,0(),z)) #98: #R2(x1,o(x2),y,z) -> #P(x1,y,0(),z) #99: #R1(o(x1),y,z) -> #o(P(x1,0(),0(),P(y,0(),0(),z))) #100: #R1(o(x1),y,z) -> #P(x1,0(),0(),P(y,0(),0(),z)) #101: #R1(o(x1),y,z) -> #P(y,0(),0(),z) #102: #P(0(),0(),0(),P(x1,x2,x3,y)) -> #o(M(x1,x2,x3,y)) #103: #P(0(),0(),0(),P(x1,x2,x3,y)) -> #M(x1,x2,x3,y) Number of SCCs: 1, DPs: 100 SCC { #1..37 #39..56 #58..61 #63..103 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... failed. Finding a loop... failed.