/export/starexec/sandbox/solver/bin/starexec_run_Default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Input TRS: 1: tower(x) -> f(a(),x,s(0())) 2: f(a(),0(),y) -> y 3: f(a(),s(x),y) -> f(b(),y,s(x)) 4: f(b(),y,x) -> f(a(),half(x),exp(y)) 5: exp(0()) -> s(0()) 6: exp(s(x)) -> double(exp(x)) 7: double(0()) -> 0() 8: double(s(x)) -> s(s(double(x))) 9: half(0()) -> double(0()) 10: half(s(0())) -> half(0()) 11: half(s(s(x))) -> s(half(x)) Number of strict rules: 11 Direct POLO(bPol) ... removes: 1 2 a w: 1 tower w: x1 + 3 s w: x1 b w: 1 f w: x1 + x2 + x3 half w: x1 0 w: 1 double w: x1 exp w: x1 Number of strict rules: 9 Direct POLO(bPol) ... failed. Uncurrying half f double 3: f^1_a(s(x),y) -> f^1_b(y,s(x)) 4: f^1_b(y,x) -> f^1_a(half(x),exp(y)) 5: exp(0()) -> s(0()) 6: exp(s(x)) -> double(exp(x)) 7: double^1_0() -> 0() 8: double^1_s(x) -> s(s(double(x))) 9: half^1_0() -> double^1_0() 10: half^1_s(0()) -> half^1_0() 11: half^1_s(s(x)) -> s(half(x)) 12: double(0()) ->= double^1_0() 13: double(s(_1)) ->= double^1_s(_1) 14: f(a(),_2,_3) ->= f^1_a(_2,_3) 15: f(b(),_2,_3) ->= f^1_b(_2,_3) 16: half(0()) ->= half^1_0() 17: half(s(_1)) ->= half^1_s(_1) Number of strict rules: 9 Direct POLO(bPol) ... removes: 15 14 a w: 1 tower w: x1 double^1_s w: x1 s w: x1 double^1_0 w: 1 b w: 1 f^1_b w: x1 + x2 + 1 half^1_s w: x1 f w: 2 * x1 + x2 + x3 half w: x1 f^1_a w: x1 + x2 + 1 0 w: 1 double w: x1 half^1_0 w: 1 exp w: x1 Number of strict rules: 9 Direct POLO(bPol) ... failed. Dependency Pairs: #1: #exp(s(x)) -> #double(exp(x)) #2: #exp(s(x)) -> #exp(x) #3: #double(s(_1)) ->? #double^1_s(_1) #4: #half^1_0() -> #double^1_0() #5: #half^1_s(s(x)) -> #half(x) #6: #double(0()) ->? #double^1_0() #7: #half^1_s(0()) -> #half^1_0() #8: #half(s(_1)) ->? #half^1_s(_1) #9: #half(0()) ->? #half^1_0() #10: #f^1_a(s(x),y) -> #f^1_b(y,s(x)) #11: #double^1_s(x) -> #double(x) #12: #f^1_b(y,x) -> #f^1_a(half(x),exp(y)) #13: #f^1_b(y,x) -> #half(x) #14: #f^1_b(y,x) -> #exp(y) Number of SCCs: 4, DPs: 7 SCC { #2 } POLO(Sum)... succeeded. a w: 0 tower w: 0 #f^1_a w: 0 double^1_s w: 0 s w: x1 + 1 #f^1_b w: 0 double^1_0 w: 0 b w: 0 f^1_b w: 0 #exp w: x1 #half w: 0 half^1_s w: 0 f w: 0 half w: 0 #double^1_0 w: 0 f^1_a w: 0 0 w: 0 #double w: 0 double w: 0 #half^1_s w: 0 half^1_0 w: 0 exp w: 0 #half^1_0 w: 0 #double^1_s w: 0 USABLE RULES: { } Removed DPs: #2 Number of SCCs: 3, DPs: 6 SCC { #3 #11 } POLO(Sum)... succeeded. a w: 0 tower w: 0 #f^1_a w: 0 double^1_s w: 0 s w: x1 + 2 #f^1_b w: 0 double^1_0 w: 0 b w: 0 f^1_b w: 0 #exp w: 0 #half w: 0 half^1_s w: 0 f w: 0 half w: 0 #double^1_0 w: 0 f^1_a w: 0 0 w: 0 #double w: x1 double w: 0 #half^1_s w: 0 half^1_0 w: 0 exp w: 0 #half^1_0 w: 0 #double^1_s w: x1 + 1 USABLE RULES: { } Removed DPs: #3 #11 Number of SCCs: 2, DPs: 4 SCC { #5 #8 } POLO(Sum)... succeeded. a w: 0 tower w: 0 #f^1_a w: 0 double^1_s w: 0 s w: x1 + 2 #f^1_b w: 0 double^1_0 w: 0 b w: 0 f^1_b w: 0 #exp w: 0 #half w: x1 + 1 half^1_s w: 0 f w: 0 half w: 0 #double^1_0 w: 0 f^1_a w: 0 0 w: 0 #double w: 0 double w: 0 #half^1_s w: x1 half^1_0 w: 0 exp w: 0 #half^1_0 w: 0 #double^1_s w: 1 USABLE RULES: { } Removed DPs: #5 #8 Number of SCCs: 1, DPs: 2 SCC { #10 #12 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... succeeded. a w: 0 tower w: 0 #f^1_a w: max(x1 - 1, 0) double^1_s w: 1 s w: max(x1 + 4, 0) #f^1_b w: max(x2 - 2, 0) double^1_0 w: 0 b w: 0 f^1_b w: 0 #exp w: 0 #half w: max(x1 - 1, 0) half^1_s w: max(x1 + 1, 0) f w: max(x2 - 1, 0) half w: max(x1 - 2, 0) #double^1_0 w: 0 f^1_a w: max(x1 - 1, 0) 0 w: 0 #double w: 0 double w: 1 #half^1_s w: max(x1 - 1, 0) half^1_0 w: 0 exp w: 1 #half^1_0 w: 0 #double^1_s w: 0 USABLE RULES: { 7 9..11 16 17 } Removed DPs: #10 Number of SCCs: 0, DPs: 0