/export/starexec/sandbox2/solver/bin/starexec_run_Default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Input TRS: 1: app(nil(),k) -> k 2: app(l,nil()) -> l 3: app(cons(x,l),k) -> cons(x,app(l,k)) 4: sum(cons(x,nil())) -> cons(x,nil()) 5: sum(cons(x,cons(y,l))) -> sum(cons(plus(x,y),l)) 6: sum(app(l,cons(x,cons(y,k)))) -> sum(app(l,sum(cons(x,cons(y,k))))) 7: plus(s(x),s(y)) -> s(s(plus(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y))))) 8: plus(s(x),x) -> plus(if(gt(x,x),id(x),id(x)),s(x)) 9: plus(zero(),y) -> y 10: plus(id(x),s(y)) -> s(plus(x,if(gt(s(y),y),y,s(y)))) 11: id(x) -> x 12: if(true(),x,y) -> x 13: if(false(),x,y) -> y 14: not(x) -> if(x,false(),true()) 15: gt(s(x),zero()) -> true() 16: gt(zero(),y) -> false() 17: gt(s(x),s(y)) -> gt(x,y) Number of strict rules: 17 Direct POLO(bPol) ... failed. Uncurrying gt 1: app(nil(),k) -> k 2: app(l,nil()) -> l 3: app(cons(x,l),k) -> cons(x,app(l,k)) 4: sum(cons(x,nil())) -> cons(x,nil()) 5: sum(cons(x,cons(y,l))) -> sum(cons(plus(x,y),l)) 6: sum(app(l,cons(x,cons(y,k)))) -> sum(app(l,sum(cons(x,cons(y,k))))) 7: plus(s(x),s(y)) -> s(s(plus(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y))))) 8: plus(s(x),x) -> plus(if(gt(x,x),id(x),id(x)),s(x)) 9: plus(zero(),y) -> y 10: plus(id(x),s(y)) -> s(plus(x,if(gt^1_s(y,y),y,s(y)))) 11: id(x) -> x 12: if(true(),x,y) -> x 13: if(false(),x,y) -> y 14: not(x) -> if(x,false(),true()) 15: gt^1_s(x,zero()) -> true() 16: gt^1_zero(y) -> false() 17: gt^1_s(x,s(y)) -> gt(x,y) 18: gt(zero(),_1) ->= gt^1_zero(_1) 19: gt(s(_1),_2) ->= gt^1_s(_1,_2) Number of strict rules: 17 Direct POLO(bPol) ... failed. Dependency Pairs: #1: #sum(app(l,cons(x,cons(y,k)))) -> #sum(app(l,sum(cons(x,cons(y,k))))) #2: #sum(app(l,cons(x,cons(y,k)))) -> #app(l,sum(cons(x,cons(y,k)))) #3: #sum(app(l,cons(x,cons(y,k)))) -> #sum(cons(x,cons(y,k))) #4: #not(x) -> #if(x,false(),true()) #5: #plus(s(x),s(y)) -> #plus(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y))) #6: #plus(s(x),s(y)) -> #if(gt(x,y),x,y) #7: #plus(s(x),s(y)) -> #gt(x,y) #8: #plus(s(x),s(y)) -> #if(not(gt(x,y)),id(x),id(y)) #9: #plus(s(x),s(y)) -> #not(gt(x,y)) #10: #plus(s(x),s(y)) -> #gt(x,y) #11: #plus(s(x),s(y)) -> #id(x) #12: #plus(s(x),s(y)) -> #id(y) #13: #plus(id(x),s(y)) -> #plus(x,if(gt^1_s(y,y),y,s(y))) #14: #plus(id(x),s(y)) -> #if(gt^1_s(y,y),y,s(y)) #15: #plus(id(x),s(y)) -> #gt^1_s(y,y) #16: #sum(cons(x,cons(y,l))) -> #sum(cons(plus(x,y),l)) #17: #sum(cons(x,cons(y,l))) -> #plus(x,y) #18: #gt^1_s(x,s(y)) -> #gt(x,y) #19: #gt(s(_1),_2) ->? #gt^1_s(_1,_2) #20: #app(cons(x,l),k) -> #app(l,k) #21: #plus(s(x),x) -> #plus(if(gt(x,x),id(x),id(x)),s(x)) #22: #plus(s(x),x) -> #if(gt(x,x),id(x),id(x)) #23: #plus(s(x),x) -> #gt(x,x) #24: #plus(s(x),x) -> #id(x) #25: #plus(s(x),x) -> #id(x) #26: #gt(zero(),_1) ->? #gt^1_zero(_1) Number of SCCs: 5, DPs: 8 SCC { #20 } POLO(Sum)... succeeded. zero w: 0 s w: 0 gt w: 0 #gt^1_zero w: 0 #plus w: 0 false w: 0 #id w: 0 gt^1_zero w: 0 true w: 0 sum w: 0 #not w: 0 if w: 0 nil w: 0 #gt w: 0 #app w: x1 plus w: 0 cons w: x2 + 1 gt^1_s w: 0 #if w: 0 id w: 0 #sum w: 0 #gt^1_s w: 0 not w: 0 app w: 0 USABLE RULES: { } Removed DPs: #20 Number of SCCs: 4, DPs: 7 SCC { #16 } POLO(Sum)... succeeded. zero w: 1 s w: x1 gt w: x2 + 1 #gt^1_zero w: 0 #plus w: 0 false w: 3 #id w: 0 gt^1_zero w: 2 true w: 1 sum w: 0 #not w: 0 if w: x1 + x2 + x3 nil w: 0 #gt w: 0 #app w: 0 plus w: x2 + 1 cons w: x2 + 1 gt^1_s w: 0 #if w: 0 id w: x1 #sum w: x1 #gt^1_s w: 0 not w: 0 app w: 0 USABLE RULES: { } Removed DPs: #16 Number of SCCs: 3, DPs: 6 SCC { #18 #19 } POLO(Sum)... succeeded. zero w: 0 s w: x1 + 1 gt w: x2 + 2 #gt^1_zero w: 0 #plus w: 0 false w: 4 #id w: 0 gt^1_zero w: 3 true w: 2 sum w: 0 #not w: 0 if w: x3 + 1 nil w: 0 #gt w: x1 + x2 #app w: 0 plus w: 1 cons w: 1 gt^1_s w: x1 + 1 #if w: 0 id w: x1 + 1 #sum w: x1 #gt^1_s w: x1 + x2 not w: 3 app w: 0 USABLE RULES: { } Removed DPs: #18 #19 Number of SCCs: 2, DPs: 4 SCC { #1 } POLO(Sum)... succeeded. zero w: 0 s w: x1 + 1 gt w: x2 + 2 #gt^1_zero w: 0 #plus w: 0 false w: 4 #id w: 0 gt^1_zero w: 3 true w: 2 sum w: 3 #not w: 0 if w: x3 + 1 nil w: 1 #gt w: 0 #app w: 0 plus w: 1 cons w: x2 + 2 gt^1_s w: x1 + 1 #if w: 0 id w: x1 + 1 #sum w: x1 #gt^1_s w: 0 not w: 3 app w: x1 + x2 + 1 USABLE RULES: { 1..5 } Removed DPs: #1 Number of SCCs: 1, DPs: 3 SCC { #5 #13 #21 } POLO(Sum)... POLO(max)... succeeded. zero w: 0 s w: x1 + 5 gt w: max(x1 + 8, x2 + 1) #gt^1_zero w: 0 #plus w: max(x1 + 4, x2 + 1) false w: 3 #id w: 0 gt^1_zero w: 2 true w: 3 sum w: 0 #not w: 0 if w: max(x2 + 1, x3) nil w: 0 #gt w: 0 #app w: 0 plus w: 0 cons w: 0 gt^1_s w: max(x1 + 8, x2 + 2) #if w: 0 id w: x1 + 3 #sum w: 0 #gt^1_s w: 0 not w: 4 app w: 0 USABLE RULES: { 11..14 } Removed DPs: #5 #21 Number of SCCs: 1, DPs: 1 SCC { #13 } POLO(Sum)... succeeded. zero w: 0 s w: 2 gt w: 1 #gt^1_zero w: 0 #plus w: x1 false w: 1 #id w: 0 gt^1_zero w: 1 true w: 1 sum w: 3 #not w: 0 if w: x2 + x3 nil w: 1 #gt w: 0 #app w: 0 plus w: 1 cons w: x2 + 2 gt^1_s w: 1 #if w: 0 id w: x1 + 1 #sum w: x1 #gt^1_s w: 0 not w: 2 app w: x1 + x2 + 1 USABLE RULES: { 1..5 11..13 15..19 } Removed DPs: #13 Number of SCCs: 0, DPs: 0