/export/starexec/sandbox/solver/bin/starexec_run_Default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Input TRS: 1: minus(x,0()) -> x 2: minus(s(x),s(y)) -> minus(x,y) 3: quot(0(),s(y)) -> 0() 4: quot(s(x),s(y)) -> s(quot(minus(x,y),s(y))) 5: minus(minus(x,y),z) -> minus(x,plus(y,z)) 6: plus(s(x),s(y)) -> s(s(plus(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y))))) 7: plus(s(x),x) -> plus(if(gt(x,x),id(x),id(x)),s(x)) 8: plus(zero(),y) -> y 9: plus(id(x),s(y)) -> s(plus(x,if(gt(s(y),y),y,s(y)))) 10: id(x) -> x 11: if(true(),x,y) -> x 12: if(false(),x,y) -> y 13: not(x) -> if(x,false(),true()) 14: gt(s(x),zero()) -> true() 15: gt(zero(),y) -> false() 16: gt(s(x),s(y)) -> gt(x,y) Number of strict rules: 16 Direct POLO(bPol) ... failed. Uncurrying gt 1: minus(x,0()) -> x 2: minus(s(x),s(y)) -> minus(x,y) 3: quot(0(),s(y)) -> 0() 4: quot(s(x),s(y)) -> s(quot(minus(x,y),s(y))) 5: minus(minus(x,y),z) -> minus(x,plus(y,z)) 6: plus(s(x),s(y)) -> s(s(plus(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y))))) 7: plus(s(x),x) -> plus(if(gt(x,x),id(x),id(x)),s(x)) 8: plus(zero(),y) -> y 9: plus(id(x),s(y)) -> s(plus(x,if(gt^1_s(y,y),y,s(y)))) 10: id(x) -> x 11: if(true(),x,y) -> x 12: if(false(),x,y) -> y 13: not(x) -> if(x,false(),true()) 14: gt^1_s(x,zero()) -> true() 15: gt^1_zero(y) -> false() 16: gt^1_s(x,s(y)) -> gt(x,y) 17: gt(zero(),_1) ->= gt^1_zero(_1) 18: gt(s(_1),_2) ->= gt^1_s(_1,_2) Number of strict rules: 16 Direct POLO(bPol) ... failed. Dependency Pairs: #1: #minus(s(x),s(y)) -> #minus(x,y) #2: #plus(s(x),s(y)) -> #plus(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y))) #3: #plus(s(x),s(y)) -> #if(gt(x,y),x,y) #4: #plus(s(x),s(y)) -> #gt(x,y) #5: #plus(s(x),s(y)) -> #if(not(gt(x,y)),id(x),id(y)) #6: #plus(s(x),s(y)) -> #not(gt(x,y)) #7: #plus(s(x),s(y)) -> #gt(x,y) #8: #plus(s(x),s(y)) -> #id(x) #9: #plus(s(x),s(y)) -> #id(y) #10: #not(x) -> #if(x,false(),true()) #11: #plus(id(x),s(y)) -> #plus(x,if(gt^1_s(y,y),y,s(y))) #12: #plus(id(x),s(y)) -> #if(gt^1_s(y,y),y,s(y)) #13: #plus(id(x),s(y)) -> #gt^1_s(y,y) #14: #plus(s(x),x) -> #plus(if(gt(x,x),id(x),id(x)),s(x)) #15: #plus(s(x),x) -> #if(gt(x,x),id(x),id(x)) #16: #plus(s(x),x) -> #gt(x,x) #17: #plus(s(x),x) -> #id(x) #18: #plus(s(x),x) -> #id(x) #19: #minus(minus(x,y),z) -> #minus(x,plus(y,z)) #20: #minus(minus(x,y),z) -> #plus(y,z) #21: #gt(zero(),_1) ->? #gt^1_zero(_1) #22: #gt^1_s(x,s(y)) -> #gt(x,y) #23: #quot(s(x),s(y)) -> #quot(minus(x,y),s(y)) #24: #quot(s(x),s(y)) -> #minus(x,y) #25: #gt(s(_1),_2) ->? #gt^1_s(_1,_2) Number of SCCs: 4, DPs: 8 SCC { #23 } POLO(Sum)... succeeded. zero w: 1 s w: x1 + 2 gt w: x1 + 2 minus w: x1 + 1 #gt^1_zero w: 0 #plus w: 0 false w: 5 #id w: 0 gt^1_zero w: x1 + 4 true w: 2 #not w: 0 0 w: 1 if w: x1 + x2 + x3 quot w: 0 #gt w: 0 #minus w: 0 plus w: 1 gt^1_s w: x1 + 1 #if w: 0 id w: x1 + 1 #quot w: x1 #gt^1_s w: 0 not w: 1 USABLE RULES: { 1 2 5 } Removed DPs: #23 Number of SCCs: 3, DPs: 7 SCC { #22 #25 } POLO(Sum)... succeeded. zero w: 1 s w: x1 + 2 gt w: x1 + 2 minus w: x1 + 1 #gt^1_zero w: 0 #plus w: 0 false w: 5 #id w: 0 gt^1_zero w: x1 + 4 true w: 2 #not w: 0 0 w: 1 if w: x1 + x2 + x3 quot w: 0 #gt w: x2 + 1 #minus w: 0 plus w: 1 gt^1_s w: x1 + 1 #if w: 0 id w: x1 + 1 #quot w: x1 #gt^1_s w: x2 not w: 1 USABLE RULES: { 1 2 5 } Removed DPs: #22 #25 Number of SCCs: 2, DPs: 5 SCC { #1 #19 } POLO(Sum)... succeeded. zero w: 1 s w: x1 + 2 gt w: x1 + 2 minus w: x1 + 1 #gt^1_zero w: 0 #plus w: 0 false w: 5 #id w: 0 gt^1_zero w: x1 + 4 true w: 2 #not w: 0 0 w: 1 if w: x1 + x2 + x3 quot w: 0 #gt w: 1 #minus w: x1 plus w: 1 gt^1_s w: x1 + 1 #if w: 0 id w: x1 + 1 #quot w: x1 #gt^1_s w: 0 not w: 1 USABLE RULES: { 1 2 5 } Removed DPs: #1 #19 Number of SCCs: 1, DPs: 3 SCC { #2 #11 #14 } POLO(Sum)... POLO(max)... succeeded. zero w: 1 s w: x1 + 5 gt w: 0 minus w: 0 #gt^1_zero w: 0 #plus w: max(x1 + 2, x2 + 1) false w: 1 #id w: 0 gt^1_zero w: 0 true w: 2 #not w: 0 0 w: 0 if w: max(x2 + 3, x3) quot w: 0 #gt w: 0 #minus w: 0 plus w: 0 gt^1_s w: max(x1 + 1, x2 + 1) #if w: 0 id w: x1 + 1 #quot w: 0 #gt^1_s w: 0 not w: 4 USABLE RULES: { 10..12 } Removed DPs: #2 #14 Number of SCCs: 1, DPs: 1 SCC { #11 } POLO(Sum)... succeeded. zero w: 1 s w: 2 gt w: 1 minus w: x1 + 1 #gt^1_zero w: 0 #plus w: x1 false w: 1 #id w: 0 gt^1_zero w: 1 true w: 1 #not w: 0 0 w: 1 if w: x2 + x3 + 1 quot w: 0 #gt w: 1 #minus w: 0 plus w: 1 gt^1_s w: 1 #if w: 0 id w: x1 + 1 #quot w: 0 #gt^1_s w: 0 not w: 3 USABLE RULES: { 10..18 } Removed DPs: #11 Number of SCCs: 0, DPs: 0