/export/starexec/sandbox2/solver/bin/starexec_run_Default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Input TRS: 1: times(x,plus(y,1())) -> plus(times(x,plus(y,times(1(),0()))),x) 2: times(x,1()) -> x 3: times(x,0()) -> 0() 4: plus(s(x),s(y)) -> s(s(plus(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y))))) 5: plus(s(x),x) -> plus(if(gt(x,x),id(x),id(x)),s(x)) 6: plus(zero(),y) -> y 7: plus(id(x),s(y)) -> s(plus(x,if(gt(s(y),y),y,s(y)))) 8: id(x) -> x 9: if(true(),x,y) -> x 10: if(false(),x,y) -> y 11: not(x) -> if(x,false(),true()) 12: gt(s(x),zero()) -> true() 13: gt(zero(),y) -> false() 14: gt(s(x),s(y)) -> gt(x,y) Number of strict rules: 14 Direct POLO(bPol) ... failed. Uncurrying gt 1: times(x,plus(y,1())) -> plus(times(x,plus(y,times(1(),0()))),x) 2: times(x,1()) -> x 3: times(x,0()) -> 0() 4: plus(s(x),s(y)) -> s(s(plus(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y))))) 5: plus(s(x),x) -> plus(if(gt(x,x),id(x),id(x)),s(x)) 6: plus(zero(),y) -> y 7: plus(id(x),s(y)) -> s(plus(x,if(gt^1_s(y,y),y,s(y)))) 8: id(x) -> x 9: if(true(),x,y) -> x 10: if(false(),x,y) -> y 11: not(x) -> if(x,false(),true()) 12: gt^1_s(x,zero()) -> true() 13: gt^1_zero(y) -> false() 14: gt^1_s(x,s(y)) -> gt(x,y) 15: gt(zero(),_1) ->= gt^1_zero(_1) 16: gt(s(_1),_2) ->= gt^1_s(_1,_2) Number of strict rules: 14 Direct POLO(bPol) ... failed. Dependency Pairs: #1: #not(x) -> #if(x,false(),true()) #2: #gt^1_s(x,s(y)) -> #gt(x,y) #3: #plus(id(x),s(y)) -> #plus(x,if(gt^1_s(y,y),y,s(y))) #4: #plus(id(x),s(y)) -> #if(gt^1_s(y,y),y,s(y)) #5: #plus(id(x),s(y)) -> #gt^1_s(y,y) #6: #plus(s(x),x) -> #plus(if(gt(x,x),id(x),id(x)),s(x)) #7: #plus(s(x),x) -> #if(gt(x,x),id(x),id(x)) #8: #plus(s(x),x) -> #gt(x,x) #9: #plus(s(x),x) -> #id(x) #10: #plus(s(x),x) -> #id(x) #11: #gt(s(_1),_2) ->? #gt^1_s(_1,_2) #12: #times(x,plus(y,1())) -> #plus(times(x,plus(y,times(1(),0()))),x) #13: #times(x,plus(y,1())) -> #times(x,plus(y,times(1(),0()))) #14: #times(x,plus(y,1())) -> #plus(y,times(1(),0())) #15: #times(x,plus(y,1())) -> #times(1(),0()) #16: #gt(zero(),_1) ->? #gt^1_zero(_1) #17: #plus(s(x),s(y)) -> #plus(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y))) #18: #plus(s(x),s(y)) -> #if(gt(x,y),x,y) #19: #plus(s(x),s(y)) -> #gt(x,y) #20: #plus(s(x),s(y)) -> #if(not(gt(x,y)),id(x),id(y)) #21: #plus(s(x),s(y)) -> #not(gt(x,y)) #22: #plus(s(x),s(y)) -> #gt(x,y) #23: #plus(s(x),s(y)) -> #id(x) #24: #plus(s(x),s(y)) -> #id(y) Number of SCCs: 3, DPs: 6 SCC { #13 } POLO(Sum)... succeeded. zero w: 1 1 w: 2 s w: 0 gt w: x1 + 2 #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 #times w: x2 0 w: 1 if w: x1 + x2 times w: x2 #gt w: 0 plus w: x2 gt^1_s w: 1 #if w: 0 id w: x1 + 1 #gt^1_s w: 0 not w: 1 USABLE RULES: { 3..7 } Removed DPs: #13 Number of SCCs: 2, DPs: 5 SCC { #2 #11 } POLO(Sum)... succeeded. zero w: 1 1 w: 2 s w: x1 + 2 gt w: x1 #gt^1_zero w: 0 #plus w: 0 false w: 3 #id w: 0 gt^1_zero w: x1 + 2 true w: 2 #not w: 0 #times w: 0 0 w: 1 if w: x1 + x2 times w: x2 #gt w: x1 plus w: x1 + x2 + 1 gt^1_s w: 1 #if w: 0 id w: 0 #gt^1_s w: x1 + 1 not w: 0 USABLE RULES: { } Removed DPs: #2 #11 Number of SCCs: 1, DPs: 3 SCC { #3 #6 #17 } POLO(Sum)... POLO(max)... succeeded. zero w: 0 1 w: 0 s w: x1 + 6 gt w: 0 #gt^1_zero w: 0 #plus w: max(x1 + 6, x2 + 2) false w: 0 #id w: 0 gt^1_zero w: 0 true w: 0 #not w: 0 #times w: 0 0 w: 0 if w: max(x1 + 1, x2 + 3, x3) times w: 0 #gt w: 0 plus w: 0 gt^1_s w: 0 #if w: 0 id w: x1 #gt^1_s w: 0 not w: x1 + 8 USABLE RULES: { 8..16 } Removed DPs: #6 #17 Number of SCCs: 1, DPs: 1 SCC { #3 } POLO(Sum)... succeeded. zero w: 1 1 w: 2 s w: x1 + 1 gt w: x1 + x2 #gt^1_zero w: 0 #plus w: x1 false w: 0 #id w: 0 gt^1_zero w: 0 true w: 1 #not w: 0 #times w: 0 0 w: 1 if w: x1 + x2 + x3 + 1 times w: x2 #gt w: 0 plus w: 1 gt^1_s w: x1 + x2 + 1 #if w: 0 id w: x1 + 1 #gt^1_s w: 1 not w: x1 + 2 USABLE RULES: { 8..10 12..16 } Removed DPs: #3 Number of SCCs: 0, DPs: 0