/export/starexec/sandbox/solver/bin/starexec_run_Default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/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: active(s(X)) -> s(active(X)) 11: active(div(X1,X2)) -> div(active(X1),X2) 12: active(if(X1,X2,X3)) -> if(active(X1),X2,X3) 13: s(mark(X)) -> mark(s(X)) 14: div(mark(X1),X2) -> mark(div(X1,X2)) 15: if(mark(X1),X2,X3) -> mark(if(X1,X2,X3)) 16: proper(minus(X1,X2)) -> minus(proper(X1),proper(X2)) 17: proper(0()) -> ok(0()) 18: proper(s(X)) -> s(proper(X)) 19: proper(geq(X1,X2)) -> geq(proper(X1),proper(X2)) 20: proper(true()) -> ok(true()) 21: proper(false()) -> ok(false()) 22: proper(div(X1,X2)) -> div(proper(X1),proper(X2)) 23: proper(if(X1,X2,X3)) -> if(proper(X1),proper(X2),proper(X3)) 24: minus(ok(X1),ok(X2)) -> ok(minus(X1,X2)) 25: s(ok(X)) -> ok(s(X)) 26: geq(ok(X1),ok(X2)) -> ok(geq(X1,X2)) 27: div(ok(X1),ok(X2)) -> ok(div(X1,X2)) 28: if(ok(X1),ok(X2),ok(X3)) -> ok(if(X1,X2,X3)) 29: top(mark(X)) -> top(proper(X)) 30: top(ok(X)) -> top(active(X)) Number of strict rules: 30 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #active(minus(s(X),s(Y))) -> #minus(X,Y) #2: #top(mark(X)) -> #top(proper(X)) #3: #top(mark(X)) -> #proper(X) #4: #s(mark(X)) -> #s(X) #5: #active(div(X1,X2)) -> #div(active(X1),X2) #6: #active(div(X1,X2)) -> #active(X1) #7: #minus(ok(X1),ok(X2)) -> #minus(X1,X2) #8: #proper(if(X1,X2,X3)) -> #if(proper(X1),proper(X2),proper(X3)) #9: #proper(if(X1,X2,X3)) -> #proper(X1) #10: #proper(if(X1,X2,X3)) -> #proper(X2) #11: #proper(if(X1,X2,X3)) -> #proper(X3) #12: #active(if(X1,X2,X3)) -> #if(active(X1),X2,X3) #13: #active(if(X1,X2,X3)) -> #active(X1) #14: #div(mark(X1),X2) -> #div(X1,X2) #15: #top(ok(X)) -> #top(active(X)) #16: #top(ok(X)) -> #active(X) #17: #s(ok(X)) -> #s(X) #18: #active(div(s(X),s(Y))) -> #if(geq(X,Y),s(div(minus(X,Y),s(Y))),0()) #19: #active(div(s(X),s(Y))) -> #geq(X,Y) #20: #active(div(s(X),s(Y))) -> #s(div(minus(X,Y),s(Y))) #21: #active(div(s(X),s(Y))) -> #div(minus(X,Y),s(Y)) #22: #active(div(s(X),s(Y))) -> #minus(X,Y) #23: #active(s(X)) -> #s(active(X)) #24: #active(s(X)) -> #active(X) #25: #active(geq(s(X),s(Y))) -> #geq(X,Y) #26: #if(ok(X1),ok(X2),ok(X3)) -> #if(X1,X2,X3) #27: #proper(div(X1,X2)) -> #div(proper(X1),proper(X2)) #28: #proper(div(X1,X2)) -> #proper(X1) #29: #proper(div(X1,X2)) -> #proper(X2) #30: #div(ok(X1),ok(X2)) -> #div(X1,X2) #31: #proper(geq(X1,X2)) -> #geq(proper(X1),proper(X2)) #32: #proper(geq(X1,X2)) -> #proper(X1) #33: #proper(geq(X1,X2)) -> #proper(X2) #34: #geq(ok(X1),ok(X2)) -> #geq(X1,X2) #35: #proper(minus(X1,X2)) -> #minus(proper(X1),proper(X2)) #36: #proper(minus(X1,X2)) -> #proper(X1) #37: #proper(minus(X1,X2)) -> #proper(X2) #38: #if(mark(X1),X2,X3) -> #if(X1,X2,X3) #39: #proper(s(X)) -> #s(proper(X)) #40: #proper(s(X)) -> #proper(X) Number of SCCs: 8, DPs: 23 SCC { #7 } POLO(Sum)... succeeded. #div w: 0 s w: 0 minus w: 0 #geq w: 0 top w: 0 false w: 0 #top w: 0 div w: 0 geq w: 0 true w: 0 proper w: 0 ok w: x1 + 1 0 w: 0 if w: 0 #s w: 0 mark w: 0 #minus w: x1 + x2 #proper w: 0 active w: 0 #if w: 0 #active w: 0 USABLE RULES: { } Removed DPs: #7 Number of SCCs: 7, DPs: 22 SCC { #34 } POLO(Sum)... succeeded. #div w: 0 s w: 0 minus w: 0 #geq w: x2 top w: 0 false w: 0 #top w: 0 div w: 0 geq w: 0 true w: 0 proper w: 0 ok w: x1 + 1 0 w: 0 if w: 0 #s w: 0 mark w: 0 #minus w: 0 #proper w: 0 active w: 0 #if w: 0 #active w: 0 USABLE RULES: { } Removed DPs: #34 Number of SCCs: 6, DPs: 21 SCC { #4 #17 } POLO(Sum)... succeeded. #div w: 0 s w: 0 minus w: 0 #geq w: 0 top w: 0 false w: 0 #top w: 0 div w: 0 geq w: 0 true w: 0 proper w: 0 ok w: x1 + 1 0 w: 0 if w: 0 #s w: x1 mark w: x1 + 1 #minus w: 0 #proper w: 0 active w: 0 #if w: 0 #active w: 0 USABLE RULES: { } Removed DPs: #4 #17 Number of SCCs: 5, DPs: 19 SCC { #2 #15 } POLO(Sum)... POLO(max)... QLPOS... succeeded. #div s: [] p: 0 s s: [1] p: 6 minus s: [1] p: 4 #geq s: [] p: 0 top s: [] p: 0 false s: [] p: 5 #top s: [1] p: 0 div s: [2,1] p: 8 geq s: [1,2] p: 4 true s: [] p: 0 proper s: 1 ok s: 1 0 s: [] p: 8 if s: [1,3,2] p: 7 #s s: [] p: 0 mark s: [1] p: 3 #minus s: [1] p: 0 #proper s: [] p: 0 active s: 1 #if s: [1,3] p: 0 #active s: [] p: 0 USABLE RULES: { 1..28 } Removed DPs: #2 Number of SCCs: 5, DPs: 18 SCC { #15 } POLO(Sum)... succeeded. #div w: 0 s w: x1 minus w: x2 #geq w: 0 top w: 0 false w: 1 #top w: x1 div w: x2 geq w: x1 true w: 1 proper w: 3 ok w: x1 + 2 0 w: 1 if w: x2 #s w: 0 mark w: 0 #minus w: 0 #proper w: 0 active w: x1 + 1 #if w: 0 #active w: 0 USABLE RULES: { 1..28 } Removed DPs: #15 Number of SCCs: 4, DPs: 17 SCC { #14 #30 } POLO(Sum)... succeeded. #div w: x2 s w: x1 minus w: x2 #geq w: 0 top w: 0 false w: 1 #top w: x1 div w: x2 geq w: x1 true w: 1 proper w: 3 ok w: x1 + 2 0 w: 1 if w: x2 #s w: 0 mark w: 0 #minus w: 0 #proper w: 0 active w: x1 + 1 #if w: 0 #active w: 0 USABLE RULES: { 1..28 } Removed DPs: #30 Number of SCCs: 4, DPs: 16 SCC { #14 } POLO(Sum)... succeeded. #div w: x1 s w: x1 minus w: x2 #geq w: 0 top w: 0 false w: 1 #top w: 0 div w: x2 geq w: x1 true w: 1 proper w: 3 ok w: x1 + 3 0 w: 1 if w: x2 #s w: 0 mark w: x1 + 1 #minus w: 0 #proper w: 0 active w: x1 + 2 #if w: 0 #active w: 0 USABLE RULES: { 1 3 4 6 8 } Removed DPs: #14 Number of SCCs: 3, DPs: 15 SCC { #6 #13 #24 } POLO(Sum)... succeeded. #div w: 0 s w: x1 + 1 minus w: x2 #geq w: 0 top w: 0 false w: 0 #top w: 0 div w: x1 + 1 geq w: x2 true w: 1 proper w: x1 + 3 ok w: x1 + 4 0 w: 1 if w: x1 + 1 #s w: 0 mark w: x1 + 1 #minus w: 0 #proper w: 0 active w: 2 #if w: 0 #active w: x1 USABLE RULES: { 1 3 4 6 24 } Removed DPs: #6 #13 #24 Number of SCCs: 2, DPs: 12 SCC { #26 #38 } POLO(Sum)... succeeded. #div w: 0 s w: x1 + 1 minus w: x2 #geq w: 0 top w: 0 false w: 0 #top w: 0 div w: x1 + 1 geq w: x2 true w: 1 proper w: x1 + 3 ok w: x1 + 4 0 w: 1 if w: x1 + 1 #s w: 0 mark w: x1 + 1 #minus w: 0 #proper w: 0 active w: 2 #if w: x1 + x3 #active w: 0 USABLE RULES: { 1 3 4 6 24 } Removed DPs: #26 #38 Number of SCCs: 1, DPs: 10 SCC { #9..11 #28 #29 #32 #33 #36 #37 #40 } POLO(Sum)... succeeded. #div w: 0 s w: x1 + 1 minus w: x1 + x2 + 1 #geq w: 0 top w: 0 false w: 1 #top w: 0 div w: x1 + x2 + 1 geq w: x1 + x2 + 1 true w: 1 proper w: x1 ok w: 2 0 w: 0 if w: x1 + x2 + x3 + 1 #s w: 0 mark w: x1 + 1 #minus w: 0 #proper w: x1 active w: 7 #if w: 0 #active w: 0 USABLE RULES: { 1 3 4 6 24 } Removed DPs: #9..11 #28 #29 #32 #33 #36 #37 #40 Number of SCCs: 0, DPs: 0