/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Input TRS: 1: 0(\#()) -> \#() 2: +(\#(),x) -> x 3: +(x,\#()) -> x 4: +(0(x),0(y)) -> 0(+(x,y)) 5: +(0(x),1(y)) -> 1(+(x,y)) 6: +(1(x),0(y)) -> 1(+(x,y)) 7: +(0(x),j(y)) -> j(+(x,y)) 8: +(j(x),0(y)) -> j(+(x,y)) 9: +(1(x),1(y)) -> j(+(+(x,y),1(\#()))) 10: +(j(x),j(y)) -> 1(+(+(x,y),j(\#()))) 11: +(1(x),j(y)) -> 0(+(x,y)) 12: +(j(x),1(y)) -> 0(+(x,y)) 13: +(+(x,y),z) -> +(x,+(y,z)) 14: opp(\#()) -> \#() 15: opp(0(x)) -> 0(opp(x)) 16: opp(1(x)) -> j(opp(x)) 17: opp(j(x)) -> 1(opp(x)) 18: -(x,y) -> +(x,opp(y)) 19: *(\#(),x) -> \#() 20: *(0(x),y) -> 0(*(x,y)) 21: *(1(x),y) -> +(0(*(x,y)),y) 22: *(j(x),y) -> -(0(*(x,y)),y) 23: *(*(x,y),z) -> *(x,*(y,z)) 24: *(+(x,y),z) -> +(*(x,z),*(y,z)) 25: *(x,+(y,z)) -> +(*(x,y),*(x,z)) Number of strict rules: 25 Direct poly ... failed. Freezing ... failed. Dependency Pairs: #1: #+(1(x),0(y)) -> #+(x,y) #2: #+(+(x,y),z) -> #+(x,+(y,z)) #3: #+(+(x,y),z) -> #+(y,z) #4: #+(1(x),1(y)) -> #+(+(x,y),1(\#())) #5: #+(1(x),1(y)) -> #+(x,y) #6: #+(1(x),j(y)) -> #0(+(x,y)) #7: #+(1(x),j(y)) -> #+(x,y) #8: #*(+(x,y),z) -> #+(*(x,z),*(y,z)) #9: #*(+(x,y),z) -> #*(x,z) #10: #*(+(x,y),z) -> #*(y,z) #11: #*(*(x,y),z) -> #*(x,*(y,z)) #12: #*(*(x,y),z) -> #*(y,z) #13: #+(j(x),1(y)) -> #0(+(x,y)) #14: #+(j(x),1(y)) -> #+(x,y) #15: #*(x,+(y,z)) -> #+(*(x,y),*(x,z)) #16: #*(x,+(y,z)) -> #*(x,y) #17: #*(x,+(y,z)) -> #*(x,z) #18: #*(0(x),y) -> #0(*(x,y)) #19: #*(0(x),y) -> #*(x,y) #20: #+(0(x),j(y)) -> #+(x,y) #21: #+(j(x),j(y)) -> #+(+(x,y),j(\#())) #22: #+(j(x),j(y)) -> #+(x,y) #23: #+(0(x),1(y)) -> #+(x,y) #24: #*(j(x),y) -> #-(0(*(x,y)),y) #25: #*(j(x),y) -> #0(*(x,y)) #26: #*(j(x),y) -> #*(x,y) #27: #opp(j(x)) -> #opp(x) #28: #*(1(x),y) -> #+(0(*(x,y)),y) #29: #*(1(x),y) -> #0(*(x,y)) #30: #*(1(x),y) -> #*(x,y) #31: #opp(1(x)) -> #opp(x) #32: #+(j(x),0(y)) -> #+(x,y) #33: #opp(0(x)) -> #0(opp(x)) #34: #opp(0(x)) -> #opp(x) #35: #+(0(x),0(y)) -> #0(+(x,y)) #36: #+(0(x),0(y)) -> #+(x,y) #37: #-(x,y) -> #+(x,opp(y)) #38: #-(x,y) -> #opp(y) Number of SCCs: 3, DPs: 25 SCC { #27 #31 #34 } Sum... succeeded. #0(x1) w: (0) 1(x1) w: (1 + x1) #*(x1,x2) w: (0) \#() w: (0) #opp(x1) w: (x1) 0(x1) w: (1 + x1) -(x1,x2) w: (0) j(x1) w: (1 + x1) opp(x1) w: (0) #-(x1,x2) w: (0) +(x1,x2) w: (0) #+(x1,x2) w: (0) *(x1,x2) w: (0) USABLE RULES: { } Removed DPs: #27 #31 #34 Number of SCCs: 2, DPs: 22 SCC { #9..12 #16 #17 #19 #26 #30 } Sum... succeeded. #0(x1) w: (0) 1(x1) w: (2 + x1) #*(x1,x2) w: (21240 + x1) \#() w: (1) #opp(x1) w: (0) 0(x1) w: (4 + x1) -(x1,x2) w: (x2 + x1) j(x1) w: (1 + x1) opp(x1) w: (1 + x1) #-(x1,x2) w: (0) +(x1,x2) w: (7720 + x2 + x1) #+(x1,x2) w: (0) *(x1,x2) w: (1 + x2 + x1) USABLE RULES: { } Removed DPs: #9..12 #19 #26 #30 Number of SCCs: 2, DPs: 15 SCC { #16 #17 } Sum... Max... succeeded. #0(x1) w: (0) 1(x1) w: (0) #*(x1,x2) w: (max{1 + x2, 0}) \#() w: (0) #opp(x1) w: (0) 0(x1) w: (0) -(x1,x2) w: (0) j(x1) w: (0) opp(x1) w: (0) #-(x1,x2) w: (0) +(x1,x2) w: (max{x2, 1 + x1}) #+(x1,x2) w: (0) *(x1,x2) w: (0) USABLE RULES: { } Removed DPs: #16 Number of SCCs: 2, DPs: 14 SCC { #17 } Sum... Max... succeeded. #0(x1) w: (0) 1(x1) w: (0) #*(x1,x2) w: (max{1 + x2, 0}) \#() w: (0) #opp(x1) w: (0) 0(x1) w: (0) -(x1,x2) w: (0) j(x1) w: (0) opp(x1) w: (0) #-(x1,x2) w: (0) +(x1,x2) w: (max{1 + x2, 0}) #+(x1,x2) w: (0) *(x1,x2) w: (0) USABLE RULES: { } Removed DPs: #17 Number of SCCs: 1, DPs: 13 SCC { #1..5 #7 #14 #20..23 #32 #36 } Sum... succeeded. #0(x1) w: (0) 1(x1) w: (2 + x1) #*(x1,x2) w: (21240) \#() w: (0) #opp(x1) w: (0) 0(x1) w: (1 + x1) -(x1,x2) w: (3 + x1) j(x1) w: (2 + x1) opp(x1) w: (844) #-(x1,x2) w: (0) +(x1,x2) w: (x2 + x1) #+(x1,x2) w: (590 + x2 + x1) *(x1,x2) w: (x2 + x1) USABLE RULES: { 1..13 } Removed DPs: #1 #4 #5 #7 #14 #20..23 #32 #36 Number of SCCs: 1, DPs: 2 SCC { #2 #3 } Sum... succeeded. #0(x1) w: (0) 1(x1) w: (5) #*(x1,x2) w: (21240) \#() w: (0) #opp(x1) w: (0) 0(x1) w: (2) -(x1,x2) w: (3 + x2) j(x1) w: (2) opp(x1) w: (1) #-(x1,x2) w: (0) +(x1,x2) w: (3 + x2 + x1) #+(x1,x2) w: (12456 + x2 + x1) *(x1,x2) w: (x1) USABLE RULES: { 1..13 } Removed DPs: #3 Number of SCCs: 1, DPs: 1 SCC { #2 } Sum... succeeded. #0(x1) w: (0) 1(x1) w: (24700) #*(x1,x2) w: (21240) \#() w: (0) #opp(x1) w: (0) 0(x1) w: (7631) -(x1,x2) w: (24698 + x2) j(x1) w: (7631) opp(x1) w: (7630) #-(x1,x2) w: (0) +(x1,x2) w: (17069 + x2 + x1) #+(x1,x2) w: (12456 + x1) *(x1,x2) w: (x1) USABLE RULES: { 1..13 } Removed DPs: #2 Number of SCCs: 0, DPs: 0