/export/starexec/sandbox2/solver/bin/starexec_run_Default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Input TRS: 1: O(0()) -> 0() 2: +(0(),x) -> x 3: +(x,0()) -> x 4: +(O(x),O(y)) -> O(+(x,y)) 5: +(O(x),I(y)) -> I(+(x,y)) 6: +(I(x),O(y)) -> I(+(x,y)) 7: +(I(x),I(y)) -> O(+(+(x,y),I(0()))) 8: +(x,+(y,z)) -> +(+(x,y),z) 9: -(x,0()) -> x 10: -(0(),x) -> 0() 11: -(O(x),O(y)) -> O(-(x,y)) 12: -(O(x),I(y)) -> I(-(-(x,y),I(1()))) 13: -(I(x),O(y)) -> I(-(x,y)) 14: -(I(x),I(y)) -> O(-(x,y)) 15: not(true()) -> false() 16: not(false()) -> true() 17: and(x,true()) -> x 18: and(x,false()) -> false() 19: if(true(),x,y) -> x 20: if(false(),x,y) -> y 21: ge(O(x),O(y)) -> ge(x,y) 22: ge(O(x),I(y)) -> not(ge(y,x)) 23: ge(I(x),O(y)) -> ge(x,y) 24: ge(I(x),I(y)) -> ge(x,y) 25: ge(x,0()) -> true() 26: ge(0(),O(x)) -> ge(0(),x) 27: ge(0(),I(x)) -> false() 28: Log'(0()) -> 0() 29: Log'(I(x)) -> +(Log'(x),I(0())) 30: Log'(O(x)) -> if(ge(x,I(0())),+(Log'(x),I(0())),0()) 31: Log(x) -> -(Log'(x),I(0())) 32: Val(L(x)) -> x 33: Val(N(x,l(),r())) -> x 34: Min(L(x)) -> x 35: Min(N(x,l(),r())) -> Min(l()) 36: Max(L(x)) -> x 37: Max(N(x,l(),r())) -> Max(r()) 38: BS(L(x)) -> true() 39: BS(N(x,l(),r())) -> and(and(ge(x,Max(l())),ge(Min(r()),x)),and(BS(l()),BS(r()))) 40: Size(L(x)) -> I(0()) 41: Size(N(x,l(),r())) -> +(+(Size(l()),Size(r())),I(1())) 42: WB(L(x)) -> true() 43: WB(N(x,l(),r())) -> and(if(ge(Size(l()),Size(r())),ge(I(0()),-(Size(l()),Size(r()))),ge(I(0()),-(Size(r()),Size(l())))),and(WB(l()),WB(r()))) Number of strict rules: 43 Direct POLO(bPol) ... removes: 18 36 32 17 34 28 33 39 31 40 38 37 41 42 35 43 1 w: 0 Log w: 2 * x1 + 2 and w: x1 + x2 + 1 r w: 0 Size w: x1 + 1 false w: 0 l w: 1 Min w: 2 * x1 O w: 2 * x1 true w: 0 Val w: x1 I w: 2 * x1 0 w: 0 if w: x1 + x2 + x3 ge w: x1 + x2 BS w: x1 + 3 - w: x1 + x2 WB w: 2 * x1 + 1 L w: x1 + 1 N w: 2 * x1 + 2 * x2 + x3 + 25 Log' w: x1 + 1 + w: x1 + x2 not w: x1 Max w: 2 * x1 Number of strict rules: 27 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #Log'(I(x)) -> #+(Log'(x),I(0())) #2: #Log'(I(x)) -> #Log'(x) #3: #+(I(x),O(y)) -> #+(x,y) #4: #-(I(x),O(y)) -> #-(x,y) #5: #-(O(x),O(y)) -> #O(-(x,y)) #6: #-(O(x),O(y)) -> #-(x,y) #7: #ge(I(x),I(y)) -> #ge(x,y) #8: #ge(I(x),O(y)) -> #ge(x,y) #9: #-(O(x),I(y)) -> #-(-(x,y),I(1())) #10: #-(O(x),I(y)) -> #-(x,y) #11: #-(I(x),I(y)) -> #O(-(x,y)) #12: #-(I(x),I(y)) -> #-(x,y) #13: #Log'(O(x)) -> #if(ge(x,I(0())),+(Log'(x),I(0())),0()) #14: #Log'(O(x)) -> #ge(x,I(0())) #15: #Log'(O(x)) -> #+(Log'(x),I(0())) #16: #Log'(O(x)) -> #Log'(x) #17: #+(I(x),I(y)) -> #O(+(+(x,y),I(0()))) #18: #+(I(x),I(y)) -> #+(+(x,y),I(0())) #19: #+(I(x),I(y)) -> #+(x,y) #20: #+(O(x),I(y)) -> #+(x,y) #21: #ge(O(x),I(y)) -> #not(ge(y,x)) #22: #ge(O(x),I(y)) -> #ge(y,x) #23: #ge(0(),O(x)) -> #ge(0(),x) #24: #ge(O(x),O(y)) -> #ge(x,y) #25: #+(x,+(y,z)) -> #+(+(x,y),z) #26: #+(x,+(y,z)) -> #+(x,y) #27: #+(O(x),O(y)) -> #O(+(x,y)) #28: #+(O(x),O(y)) -> #+(x,y) Number of SCCs: 5, DPs: 19 SCC { #23 } POLO(Sum)... succeeded. 1 w: 0 #O w: 0 Log w: 0 and w: 0 r w: 0 Size w: 0 false w: 0 l w: 0 #ge w: x2 #Log' w: 0 Min w: 0 O w: x1 + 1 true w: 0 Val w: 0 #not w: 0 I w: 0 0 w: 0 if w: 0 ge w: 0 BS w: 0 - w: 0 WB w: 0 L w: 0 N w: 0 #- w: 0 #if w: 0 Log' w: 0 + w: 0 #+ w: 0 not w: 0 Max w: 0 USABLE RULES: { } Removed DPs: #23 Number of SCCs: 4, DPs: 18 SCC { #2 #16 } POLO(Sum)... succeeded. 1 w: 0 #O w: 0 Log w: 0 and w: 0 r w: 0 Size w: 0 false w: 0 l w: 0 #ge w: 0 #Log' w: x1 Min w: 0 O w: x1 + 1 true w: 0 Val w: 0 #not w: 0 I w: x1 + 1 0 w: 0 if w: 0 ge w: 0 BS w: 0 - w: 0 WB w: 0 L w: 0 N w: 0 #- w: 0 #if w: 0 Log' w: 0 + w: 0 #+ w: 0 not w: 0 Max w: 0 USABLE RULES: { } Removed DPs: #2 #16 Number of SCCs: 3, DPs: 16 SCC { #7 #8 #22 #24 } POLO(Sum)... succeeded. 1 w: 0 #O w: 0 Log w: 0 and w: 0 r w: 0 Size w: 0 false w: 0 l w: 0 #ge w: x1 + x2 #Log' w: 0 Min w: 0 O w: x1 + 1 true w: 0 Val w: 0 #not w: 0 I w: x1 + 1 0 w: 0 if w: 0 ge w: 0 BS w: 0 - w: 0 WB w: 0 L w: 0 N w: 0 #- w: 0 #if w: 0 Log' w: 0 + w: 0 #+ w: 0 not w: 0 Max w: 0 USABLE RULES: { } Removed DPs: #7 #8 #22 #24 Number of SCCs: 2, DPs: 12 SCC { #4 #6 #9 #10 #12 } POLO(Sum)... succeeded. 1 w: 0 #O w: 0 Log w: 0 and w: 0 r w: 0 Size w: 0 false w: 0 l w: 0 #ge w: 0 #Log' w: 0 Min w: 0 O w: x1 + 1 true w: 0 Val w: 0 #not w: 0 I w: x1 + 1 0 w: 1 if w: 0 ge w: 0 BS w: 0 - w: x1 + x2 + 1 WB w: 0 L w: 0 N w: 0 #- w: x2 #if w: 0 Log' w: 0 + w: 0 #+ w: 0 not w: 0 Max w: 0 USABLE RULES: { } Removed DPs: #4 #6 #10 #12 Number of SCCs: 2, DPs: 8 SCC { #9 } POLO(Sum)... succeeded. 1 w: 0 #O w: 0 Log w: 0 and w: 0 r w: 0 Size w: 0 false w: 0 l w: 0 #ge w: 0 #Log' w: 0 Min w: 0 O w: x1 + 2 true w: 0 Val w: 0 #not w: 0 I w: x1 + 1 0 w: 1 if w: 0 ge w: 0 BS w: 0 - w: x1 + x2 + 1 WB w: 0 L w: 0 N w: 0 #- w: x1 + x2 #if w: 0 Log' w: 0 + w: 0 #+ w: 0 not w: 0 Max w: 0 USABLE RULES: { 1 9..14 } Removed DPs: #9 Number of SCCs: 1, DPs: 7 SCC { #3 #18..20 #25 #26 #28 } POLO(Sum)... succeeded. 1 w: 0 #O w: 0 Log w: 0 and w: 0 r w: 0 Size w: 0 false w: 0 l w: 0 #ge w: 0 #Log' w: 0 Min w: 0 O w: x1 + 2 true w: 0 Val w: 0 #not w: 0 I w: x1 + 1 0 w: 0 if w: 0 ge w: 0 BS w: 0 - w: x1 + x2 + 1 WB w: 0 L w: 0 N w: 0 #- w: 0 #if w: 0 Log' w: 0 + w: x1 + x2 + 1 #+ w: x2 not w: 0 Max w: 0 USABLE RULES: { 1 9 10 } Removed DPs: #3 #19 #20 #25 #26 #28 Number of SCCs: 1, DPs: 1 SCC { #18 } POLO(Sum)... succeeded. 1 w: 1 #O w: 0 Log w: 0 and w: 0 r w: 0 Size w: 0 false w: 0 l w: 0 #ge w: 0 #Log' w: 0 Min w: 0 O w: x1 + 2 true w: 0 Val w: 0 #not w: 0 I w: x1 + 4 0 w: 1 if w: 0 ge w: 0 BS w: 0 - w: x2 + 1 WB w: 0 L w: 0 N w: 0 #- w: 0 #if w: 0 Log' w: 0 + w: x1 + x2 + 1 #+ w: x1 + x2 not w: 0 Max w: 0 USABLE RULES: { 1..8 10 } Removed DPs: #18 Number of SCCs: 0, DPs: 0