/export/starexec/sandbox2/solver/bin/starexec_run_Default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Input TRS: 1: active(minus(0(),Y)) -> mark(0()) 2: active(minus(s(X),s(Y))) -> mark(minus(X,Y)) 3: active(geq(X,0())) -> mark(true()) 4: active(geq(0(),s(Y))) -> mark(false()) 5: active(geq(s(X),s(Y))) -> mark(geq(X,Y)) 6: active(div(0(),s(Y))) -> mark(0()) 7: active(div(s(X),s(Y))) -> mark(if(geq(X,Y),s(div(minus(X,Y),s(Y))),0())) 8: active(if(true(),X,Y)) -> mark(X) 9: active(if(false(),X,Y)) -> mark(Y) 10: mark(minus(X1,X2)) -> active(minus(X1,X2)) 11: mark(0()) -> active(0()) 12: mark(s(X)) -> active(s(mark(X))) 13: mark(geq(X1,X2)) -> active(geq(X1,X2)) 14: mark(true()) -> active(true()) 15: mark(false()) -> active(false()) 16: mark(div(X1,X2)) -> active(div(mark(X1),X2)) 17: mark(if(X1,X2,X3)) -> active(if(mark(X1),X2,X3)) 18: minus(mark(X1),X2) -> minus(X1,X2) 19: minus(X1,mark(X2)) -> minus(X1,X2) 20: minus(active(X1),X2) -> minus(X1,X2) 21: minus(X1,active(X2)) -> minus(X1,X2) 22: s(mark(X)) -> s(X) 23: s(active(X)) -> s(X) 24: geq(mark(X1),X2) -> geq(X1,X2) 25: geq(X1,mark(X2)) -> geq(X1,X2) 26: geq(active(X1),X2) -> geq(X1,X2) 27: geq(X1,active(X2)) -> geq(X1,X2) 28: div(mark(X1),X2) -> div(X1,X2) 29: div(X1,mark(X2)) -> div(X1,X2) 30: div(active(X1),X2) -> div(X1,X2) 31: div(X1,active(X2)) -> div(X1,X2) 32: if(mark(X1),X2,X3) -> if(X1,X2,X3) 33: if(X1,mark(X2),X3) -> if(X1,X2,X3) 34: if(X1,X2,mark(X3)) -> if(X1,X2,X3) 35: if(active(X1),X2,X3) -> if(X1,X2,X3) 36: if(X1,active(X2),X3) -> if(X1,X2,X3) 37: if(X1,X2,active(X3)) -> if(X1,X2,X3) Number of strict rules: 37 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #active(minus(s(X),s(Y))) -> #mark(minus(X,Y)) #2: #active(minus(s(X),s(Y))) -> #minus(X,Y) #3: #div(X1,mark(X2)) -> #div(X1,X2) #4: #if(active(X1),X2,X3) -> #if(X1,X2,X3) #5: #if(X1,X2,active(X3)) -> #if(X1,X2,X3) #6: #active(div(0(),s(Y))) -> #mark(0()) #7: #mark(geq(X1,X2)) -> #active(geq(X1,X2)) #8: #active(if(false(),X,Y)) -> #mark(Y) #9: #mark(0()) -> #active(0()) #10: #geq(mark(X1),X2) -> #geq(X1,X2) #11: #s(active(X)) -> #s(X) #12: #mark(s(X)) -> #active(s(mark(X))) #13: #mark(s(X)) -> #s(mark(X)) #14: #mark(s(X)) -> #mark(X) #15: #div(X1,active(X2)) -> #div(X1,X2) #16: #mark(true()) -> #active(true()) #17: #div(active(X1),X2) -> #div(X1,X2) #18: #geq(X1,mark(X2)) -> #geq(X1,X2) #19: #minus(active(X1),X2) -> #minus(X1,X2) #20: #active(div(s(X),s(Y))) -> #mark(if(geq(X,Y),s(div(minus(X,Y),s(Y))),0())) #21: #active(div(s(X),s(Y))) -> #if(geq(X,Y),s(div(minus(X,Y),s(Y))),0()) #22: #active(div(s(X),s(Y))) -> #geq(X,Y) #23: #active(div(s(X),s(Y))) -> #s(div(minus(X,Y),s(Y))) #24: #active(div(s(X),s(Y))) -> #div(minus(X,Y),s(Y)) #25: #active(div(s(X),s(Y))) -> #minus(X,Y) #26: #mark(minus(X1,X2)) -> #active(minus(X1,X2)) #27: #if(X1,mark(X2),X3) -> #if(X1,X2,X3) #28: #active(geq(s(X),s(Y))) -> #mark(geq(X,Y)) #29: #active(geq(s(X),s(Y))) -> #geq(X,Y) #30: #div(mark(X1),X2) -> #div(X1,X2) #31: #s(mark(X)) -> #s(X) #32: #if(X1,X2,mark(X3)) -> #if(X1,X2,X3) #33: #geq(X1,active(X2)) -> #geq(X1,X2) #34: #mark(if(X1,X2,X3)) -> #active(if(mark(X1),X2,X3)) #35: #mark(if(X1,X2,X3)) -> #if(mark(X1),X2,X3) #36: #mark(if(X1,X2,X3)) -> #mark(X1) #37: #if(mark(X1),X2,X3) -> #if(X1,X2,X3) #38: #minus(X1,mark(X2)) -> #minus(X1,X2) #39: #geq(active(X1),X2) -> #geq(X1,X2) #40: #if(X1,active(X2),X3) -> #if(X1,X2,X3) #41: #minus(X1,active(X2)) -> #minus(X1,X2) #42: #mark(div(X1,X2)) -> #active(div(mark(X1),X2)) #43: #mark(div(X1,X2)) -> #div(mark(X1),X2) #44: #mark(div(X1,X2)) -> #mark(X1) #45: #active(geq(X,0())) -> #mark(true()) #46: #active(minus(0(),Y)) -> #mark(0()) #47: #active(if(true(),X,Y)) -> #mark(X) #48: #mark(false()) -> #active(false()) #49: #active(geq(0(),s(Y))) -> #mark(false()) #50: #minus(mark(X1),X2) -> #minus(X1,X2) Number of SCCs: 8, DPs: 32 SCC { #11 #31 } POLO(Sum)... succeeded. #div w: 0 s w: 0 minus w: 0 #geq w: 0 false w: 0 div w: 0 geq w: 0 true w: 0 #mark w: 0 0 w: 0 if w: 0 #s w: x1 mark w: x1 + 1 #minus w: 0 active w: x1 + 1 #if w: 0 #active w: 0 USABLE RULES: { } Removed DPs: #11 #31 Number of SCCs: 7, DPs: 30 SCC { #7 #28 } POLO(Sum)... succeeded. #div w: 0 s w: x1 + 1 minus w: 0 #geq w: 0 false w: 0 div w: 0 geq w: x1 + x2 + 1 true w: 0 #mark w: x1 + 1 0 w: 0 if w: 0 #s w: 0 mark w: x1 + 1 #minus w: 0 active w: x1 + 1 #if w: 0 #active w: x1 USABLE RULES: { 24..27 } Removed DPs: #7 #28 Number of SCCs: 6, DPs: 28 SCC { #1 #26 } POLO(Sum)... succeeded. #div w: 0 s w: x1 + 1 minus w: x1 + x2 + 1 #geq w: 0 false w: 0 div w: 0 geq w: x1 + x2 + 1 true w: 0 #mark w: x1 + 1 0 w: 0 if w: 0 #s w: 0 mark w: x1 + 1 #minus w: 0 active w: x1 + 1 #if w: 0 #active w: x1 USABLE RULES: { 18..21 24..27 } Removed DPs: #1 #26 Number of SCCs: 5, DPs: 26 SCC { #10 #18 #33 #39 } POLO(Sum)... succeeded. #div w: 0 s w: 1 minus w: x1 + x2 + 1 #geq w: x1 + x2 false w: 0 div w: 0 geq w: x1 + x2 + 1 true w: 0 #mark w: x1 + 1 0 w: 0 if w: 0 #s w: 0 mark w: x1 + 1 #minus w: 0 active w: x1 + 1 #if w: 0 #active w: x1 USABLE RULES: { 18..21 24..27 } Removed DPs: #10 #18 #33 #39 Number of SCCs: 4, DPs: 22 SCC { #19 #38 #41 #50 } POLO(Sum)... succeeded. #div w: 0 s w: 1 minus w: x1 + x2 + 1 #geq w: 0 false w: 0 div w: 0 geq w: x1 + x2 + 1 true w: 0 #mark w: x1 + 1 0 w: 0 if w: 0 #s w: 0 mark w: x1 + 1 #minus w: x1 + x2 active w: x1 + 1 #if w: 0 #active w: x1 USABLE RULES: { 18..21 24..27 } Removed DPs: #19 #38 #41 #50 Number of SCCs: 3, DPs: 18 SCC { #3 #15 #17 #30 } POLO(Sum)... succeeded. #div w: x1 + x2 s w: 1 minus w: x1 + x2 + 1 #geq w: 0 false w: 0 div w: 0 geq w: x1 + x2 + 1 true w: 0 #mark w: x1 + 1 0 w: 0 if w: 0 #s w: 0 mark w: x1 + 1 #minus w: 0 active w: x1 + 1 #if w: 0 #active w: x1 USABLE RULES: { 18..21 24..27 } Removed DPs: #3 #15 #17 #30 Number of SCCs: 2, DPs: 14 SCC { #4 #5 #27 #32 #37 #40 } POLO(Sum)... succeeded. #div w: 0 s w: 1 minus w: x1 + x2 + 1 #geq w: 0 false w: 0 div w: 0 geq w: x1 + x2 + 1 true w: 0 #mark w: x1 + 1 0 w: 0 if w: 0 #s w: 0 mark w: x1 + 1 #minus w: 0 active w: x1 + 1 #if w: x1 + x2 + x3 #active w: x1 USABLE RULES: { 18..21 24..27 } Removed DPs: #4 #5 #27 #32 #37 #40 Number of SCCs: 1, DPs: 8 SCC { #8 #14 #20 #34 #36 #42 #44 #47 } POLO(Sum)... succeeded. #div w: 0 s w: x1 + 1 minus w: 0 #geq w: 0 false w: 0 div w: x1 + x2 + 1 geq w: 0 true w: 0 #mark w: x1 0 w: 0 if w: x1 + x2 + x3 #s w: 0 mark w: x1 #minus w: 0 active w: x1 #if w: 0 #active w: x1 USABLE RULES: { 1..37 } Removed DPs: #14 #44 Number of SCCs: 1, DPs: 6 SCC { #8 #20 #34 #36 #42 #47 } POLO(Sum)... succeeded. #div w: 0 s w: 1 minus w: 0 #geq w: 0 false w: 0 div w: x1 + x2 + 3 geq w: 0 true w: 0 #mark w: x1 + 1 0 w: 0 if w: x1 + x2 + x3 + 2 #s w: 0 mark w: x1 #minus w: 0 active w: x1 #if w: 0 #active w: x1 USABLE RULES: { 1..37 } Removed DPs: #8 #20 #34 #36 #42 #47 Number of SCCs: 0, DPs: 0