/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(app(eq(),0()),0()) -> true() 2: app(app(eq(),0()),app(s(),x)) -> false() 3: app(app(eq(),app(s(),x)),0()) -> false() 4: app(app(eq(),app(s(),x)),app(s(),y)) -> app(app(eq(),x),y) 5: app(app(or(),true()),y) -> true() 6: app(app(or(),false()),y) -> y 7: app(app(union(),empty()),h) -> h 8: app(app(union(),app(app(app(edge(),x),y),i)),h) -> app(app(app(edge(),x),y),app(app(union(),i),h)) 9: app(app(app(app(reach(),x),y),empty()),h) -> false() 10: app(app(app(app(reach(),x),y),app(app(app(edge(),u),v),i)),h) -> app(app(app(app(app(if_reach_1(),app(app(eq(),x),u)),x),y),app(app(app(edge(),u),v),i)),h) 11: app(app(app(app(app(if_reach_1(),true()),x),y),app(app(app(edge(),u),v),i)),h) -> app(app(app(app(app(if_reach_2(),app(app(eq(),y),v)),x),y),app(app(app(edge(),u),v),i)),h) 12: app(app(app(app(app(if_reach_1(),false()),x),y),app(app(app(edge(),u),v),i)),h) -> app(app(app(app(reach(),x),y),i),app(app(app(edge(),u),v),h)) 13: app(app(app(app(app(if_reach_2(),true()),x),y),app(app(app(edge(),u),v),i)),h) -> true() 14: app(app(app(app(app(if_reach_2(),false()),x),y),app(app(app(edge(),u),v),i)),h) -> app(app(or(),app(app(app(app(reach(),x),y),i),h)),app(app(app(app(reach(),v),y),app(app(union(),i),h)),empty())) 15: app(app(map(),f),nil()) -> nil() 16: app(app(map(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(f,x)),app(app(map(),f),xs)) 17: app(app(filter(),f),nil()) -> nil() 18: app(app(filter(),f),app(app(cons(),x),xs)) -> app(app(app(app(filter2(),app(f,x)),f),x),xs) 19: app(app(app(app(filter2(),true()),f),x),xs) -> app(app(cons(),x),app(app(filter(),f),xs)) 20: app(app(app(app(filter2(),false()),f),x),xs) -> app(app(filter(),f),xs) Number of strict rules: 20 Direct POLO(bPol) ... failed. Uncurrying app 1: app^2_eq(0(),0()) -> true() 2: app^2_eq(0(),app^1_s(x)) -> false() 3: app^2_eq(app^1_s(x),0()) -> false() 4: app^2_eq(app^1_s(x),app^1_s(y)) -> app^2_eq(x,y) 5: app^2_or(true(),y) -> true() 6: app^2_or(false(),y) -> y 7: app^2_union(empty(),h) -> h 8: app^2_union(app^3_edge(x,y,i),h) -> app^3_edge(x,y,app^2_union(i,h)) 9: app^4_reach(x,y,empty(),h) -> false() 10: app^4_reach(x,y,app^3_edge(u,v,i),h) -> app^5_if_reach_1(app^2_eq(x,u),x,y,app^3_edge(u,v,i),h) 11: app^5_if_reach_1(true(),x,y,app^3_edge(u,v,i),h) -> app^5_if_reach_2(app^2_eq(y,v),x,y,app^3_edge(u,v,i),h) 12: app^5_if_reach_1(false(),x,y,app^3_edge(u,v,i),h) -> app^4_reach(x,y,i,app^3_edge(u,v,h)) 13: app^5_if_reach_2(true(),x,y,app^3_edge(u,v,i),h) -> true() 14: app^5_if_reach_2(false(),x,y,app^3_edge(u,v,i),h) -> app^2_or(app^4_reach(x,y,i,h),app^4_reach(v,y,app^2_union(i,h),empty())) 15: app^2_map(f,nil()) -> nil() 16: app^2_map(f,app^2_cons(x,xs)) -> app^2_cons(app(f,x),app^2_map(f,xs)) 17: app^2_filter(f,nil()) -> nil() 18: app^2_filter(f,app^2_cons(x,xs)) -> app^4_filter2(app(f,x),f,x,xs) 19: app^4_filter2(true(),f,x,xs) -> app^2_cons(x,app^2_filter(f,xs)) 20: app^4_filter2(false(),f,x,xs) -> app^2_filter(f,xs) 21: app(eq(),_1) ->= app^1_eq(_1) 22: app(app^1_eq(_1),_2) ->= app^2_eq(_1,_2) 23: app(cons(),_1) ->= app^1_cons(_1) 24: app(app^1_cons(_1),_2) ->= app^2_cons(_1,_2) 25: app(s(),_1) ->= app^1_s(_1) 26: app(union(),_1) ->= app^1_union(_1) 27: app(app^1_union(_1),_2) ->= app^2_union(_1,_2) 28: app(filter(),_1) ->= app^1_filter(_1) 29: app(app^1_filter(_1),_2) ->= app^2_filter(_1,_2) 30: app(if_reach_1(),_1) ->= app^1_if_reach_1(_1) 31: app(app^1_if_reach_1(_1),_2) ->= app^2_if_reach_1(_1,_2) 32: app(app^2_if_reach_1(_1,_2),_3) ->= app^3_if_reach_1(_1,_2,_3) 33: app(app^3_if_reach_1(_1,_2,_3),_4) ->= app^4_if_reach_1(_1,_2,_3,_4) 34: app(app^4_if_reach_1(_1,_2,_3,_4),_5) ->= app^5_if_reach_1(_1,_2,_3,_4,_5) 35: app(or(),_1) ->= app^1_or(_1) 36: app(app^1_or(_1),_2) ->= app^2_or(_1,_2) 37: app(map(),_1) ->= app^1_map(_1) 38: app(app^1_map(_1),_2) ->= app^2_map(_1,_2) 39: app(edge(),_1) ->= app^1_edge(_1) 40: app(app^1_edge(_1),_2) ->= app^2_edge(_1,_2) 41: app(app^2_edge(_1,_2),_3) ->= app^3_edge(_1,_2,_3) 42: app(reach(),_1) ->= app^1_reach(_1) 43: app(app^1_reach(_1),_2) ->= app^2_reach(_1,_2) 44: app(app^2_reach(_1,_2),_3) ->= app^3_reach(_1,_2,_3) 45: app(app^3_reach(_1,_2,_3),_4) ->= app^4_reach(_1,_2,_3,_4) 46: app(if_reach_2(),_1) ->= app^1_if_reach_2(_1) 47: app(app^1_if_reach_2(_1),_2) ->= app^2_if_reach_2(_1,_2) 48: app(app^2_if_reach_2(_1,_2),_3) ->= app^3_if_reach_2(_1,_2,_3) 49: app(app^3_if_reach_2(_1,_2,_3),_4) ->= app^4_if_reach_2(_1,_2,_3,_4) 50: app(app^4_if_reach_2(_1,_2,_3,_4),_5) ->= app^5_if_reach_2(_1,_2,_3,_4,_5) 51: app(filter2(),_1) ->= app^1_filter2(_1) 52: app(app^1_filter2(_1),_2) ->= app^2_filter2(_1,_2) 53: app(app^2_filter2(_1,_2),_3) ->= app^3_filter2(_1,_2,_3) 54: app(app^3_filter2(_1,_2,_3),_4) ->= app^4_filter2(_1,_2,_3,_4) Number of strict rules: 20 Direct POLO(bPol) ... failed. Dependency Pairs: #1: #app(app^1_filter(_1),_2) ->? #app^2_filter(_1,_2) #2: #app(app^1_map(_1),_2) ->? #app^2_map(_1,_2) #3: #app^5_if_reach_1(true(),x,y,app^3_edge(u,v,i),h) -> #app^5_if_reach_2(app^2_eq(y,v),x,y,app^3_edge(u,v,i),h) #4: #app^5_if_reach_1(true(),x,y,app^3_edge(u,v,i),h) -> #app^2_eq(y,v) #5: #app(app^3_reach(_1,_2,_3),_4) ->? #app^4_reach(_1,_2,_3,_4) #6: #app^5_if_reach_1(false(),x,y,app^3_edge(u,v,i),h) -> #app^4_reach(x,y,i,app^3_edge(u,v,h)) #7: #app^5_if_reach_2(false(),x,y,app^3_edge(u,v,i),h) -> #app^2_or(app^4_reach(x,y,i,h),app^4_reach(v,y,app^2_union(i,h),empty())) #8: #app^5_if_reach_2(false(),x,y,app^3_edge(u,v,i),h) -> #app^4_reach(x,y,i,h) #9: #app^5_if_reach_2(false(),x,y,app^3_edge(u,v,i),h) -> #app^4_reach(v,y,app^2_union(i,h),empty()) #10: #app^5_if_reach_2(false(),x,y,app^3_edge(u,v,i),h) -> #app^2_union(i,h) #11: #app^4_filter2(false(),f,x,xs) -> #app^2_filter(f,xs) #12: #app^4_reach(x,y,app^3_edge(u,v,i),h) -> #app^5_if_reach_1(app^2_eq(x,u),x,y,app^3_edge(u,v,i),h) #13: #app^4_reach(x,y,app^3_edge(u,v,i),h) -> #app^2_eq(x,u) #14: #app(app^1_eq(_1),_2) ->? #app^2_eq(_1,_2) #15: #app(app^4_if_reach_1(_1,_2,_3,_4),_5) ->? #app^5_if_reach_1(_1,_2,_3,_4,_5) #16: #app(app^1_union(_1),_2) ->? #app^2_union(_1,_2) #17: #app^4_filter2(true(),f,x,xs) -> #app^2_filter(f,xs) #18: #app(app^1_or(_1),_2) ->? #app^2_or(_1,_2) #19: #app^2_map(f,app^2_cons(x,xs)) -> #app(f,x) #20: #app^2_map(f,app^2_cons(x,xs)) -> #app^2_map(f,xs) #21: #app(app^3_filter2(_1,_2,_3),_4) ->? #app^4_filter2(_1,_2,_3,_4) #22: #app^2_union(app^3_edge(x,y,i),h) -> #app^2_union(i,h) #23: #app^2_eq(app^1_s(x),app^1_s(y)) -> #app^2_eq(x,y) #24: #app(app^4_if_reach_2(_1,_2,_3,_4),_5) ->? #app^5_if_reach_2(_1,_2,_3,_4,_5) #25: #app^2_filter(f,app^2_cons(x,xs)) -> #app^4_filter2(app(f,x),f,x,xs) #26: #app^2_filter(f,app^2_cons(x,xs)) -> #app(f,x) Number of SCCs: 4, DPs: 16 SCC { #23 } POLO(Sum)... succeeded. #app^4_reach w: 0 s w: 0 app^1_reach w: 0 app^2_edge w: 0 app^1_cons w: 0 app^1_union w: 0 #app^2_map w: 0 app^4_if_reach_2 w: 0 app^3_reach w: 0 edge w: 0 app^2_filter2 w: 0 app^4_filter2 w: 0 eq w: 0 app^5_if_reach_1 w: 0 app^4_if_reach_1 w: 0 false w: 0 app^2_if_reach_1 w: 0 app^1_if_reach_1 w: 0 app^2_or w: 0 app^3_if_reach_1 w: 0 reach w: 0 if_reach_2 w: 0 app^1_filter2 w: 0 true w: 0 #app^2_or w: 0 filter2 w: 0 #app^2_union w: 0 0 w: 0 app^3_edge w: 0 app^1_edge w: 0 #app^4_filter2 w: 0 union w: 0 nil w: 0 or w: 0 app^3_if_reach_2 w: 0 #app w: 0 app^4_reach w: 0 map w: 0 app^1_filter w: 0 #app^5_if_reach_1 w: 0 #app^2_eq w: x1 + x2 app^2_reach w: 0 app^5_if_reach_2 w: 0 cons w: 0 empty w: 0 app^1_or w: 0 app^2_eq w: 0 #app^5_if_reach_2 w: 0 filter w: 0 if_reach_1 w: 0 app^3_filter2 w: 0 app^2_filter w: 0 app^2_if_reach_2 w: 0 app^2_union w: 0 app^1_map w: 0 app^1_if_reach_2 w: 0 app^2_cons w: 0 app^1_eq w: 0 app^1_s w: x1 + 1 app^2_map w: 0 #app^2_filter w: 0 app w: 0 USABLE RULES: { } Removed DPs: #23 Number of SCCs: 3, DPs: 15 SCC { #22 } POLO(Sum)... succeeded. #app^4_reach w: 0 s w: 0 app^1_reach w: 0 app^2_edge w: 0 app^1_cons w: 0 app^1_union w: 0 #app^2_map w: 0 app^4_if_reach_2 w: 0 app^3_reach w: 0 edge w: 0 app^2_filter2 w: 0 app^4_filter2 w: 0 eq w: 0 app^5_if_reach_1 w: 0 app^4_if_reach_1 w: 0 false w: 0 app^2_if_reach_1 w: 0 app^1_if_reach_1 w: 0 app^2_or w: 0 app^3_if_reach_1 w: 0 reach w: 0 if_reach_2 w: 0 app^1_filter2 w: 0 true w: 0 #app^2_or w: 0 filter2 w: 0 #app^2_union w: x1 0 w: 0 app^3_edge w: x3 + 1 app^1_edge w: 0 #app^4_filter2 w: 0 union w: 0 nil w: 0 or w: 0 app^3_if_reach_2 w: 0 #app w: 0 app^4_reach w: 0 map w: 0 app^1_filter w: 0 #app^5_if_reach_1 w: 0 #app^2_eq w: 0 app^2_reach w: 0 app^5_if_reach_2 w: 0 cons w: 0 empty w: 0 app^1_or w: 0 app^2_eq w: 0 #app^5_if_reach_2 w: 0 filter w: 0 if_reach_1 w: 0 app^3_filter2 w: 0 app^2_filter w: 0 app^2_if_reach_2 w: 0 app^2_union w: 0 app^1_map w: 0 app^1_if_reach_2 w: 0 app^2_cons w: 0 app^1_eq w: 0 app^1_s w: 1 app^2_map w: 0 #app^2_filter w: 0 app w: 0 USABLE RULES: { } Removed DPs: #22 Number of SCCs: 2, DPs: 14 SCC { #1 #2 #11 #17 #19..21 #25 #26 } POLO(Sum)... succeeded. #app^4_reach w: 0 s w: 1 app^1_reach w: x1 + 1 app^2_edge w: x1 + x2 + 1 app^1_cons w: x1 + 1 app^1_union w: x1 + 1 #app^2_map w: x1 + x2 app^4_if_reach_2 w: x1 + x2 + x3 + 3 app^3_reach w: x1 + x2 + x3 + 3 edge w: 1 app^2_filter2 w: x1 + x2 + 2 app^4_filter2 w: x1 + x3 + x4 + 5 eq w: 1 app^5_if_reach_1 w: x1 + x3 + x4 + x5 + 5 app^4_if_reach_1 w: x1 + x3 + 3 false w: 5 app^2_if_reach_1 w: x2 + 1 app^1_if_reach_1 w: x1 + 1 app^2_or w: x2 + 2 app^3_if_reach_1 w: x2 + 1 reach w: 1 if_reach_2 w: 1 app^1_filter2 w: x1 + 1 true w: 6 #app^2_or w: 0 filter2 w: 1 #app^2_union w: 0 0 w: 1 app^3_edge w: x3 + 1 app^1_edge w: x1 + 1 #app^4_filter2 w: x2 + x3 + x4 + 2 union w: 1 nil w: 2 or w: 1 app^3_if_reach_2 w: 1 #app w: x1 + x2 app^4_reach w: x3 + x4 + 1 map w: 1 app^1_filter w: x1 + 3 #app^5_if_reach_1 w: 0 #app^2_eq w: 0 app^2_reach w: 1 app^5_if_reach_2 w: x3 + x5 + 5 cons w: 1 empty w: 1 app^1_or w: x1 + 1 app^2_eq w: x1 + 3 #app^5_if_reach_2 w: 0 filter w: 1 if_reach_1 w: 1 app^3_filter2 w: x1 + x2 + x3 + 3 app^2_filter w: 1 app^2_if_reach_2 w: x1 + x2 + 1 app^2_union w: x1 + 1 app^1_map w: x1 + 1 app^1_if_reach_2 w: x1 + 1 app^2_cons w: x1 + x2 + 2 app^1_eq w: 1 app^1_s w: x1 + 1 app^2_map w: 1 #app^2_filter w: x1 + x2 + 1 app w: x1 + x2 + 1 USABLE RULES: { } Removed DPs: #1 #2 #11 #17 #19..21 #25 #26 Number of SCCs: 1, DPs: 5 SCC { #3 #6 #8 #9 #12 } POLO(Sum)... succeeded. #app^4_reach w: x2 + x3 + x4 + 1 s w: 1 app^1_reach w: x1 + 1 app^2_edge w: x1 + x2 + 3 app^1_cons w: x1 + 1 app^1_union w: x1 + 1 #app^2_map w: 0 app^4_if_reach_2 w: x1 + x2 + x3 + 3 app^3_reach w: x1 + x2 + x3 + 3 edge w: 1 app^2_filter2 w: x1 + x2 + 2 app^4_filter2 w: x1 + x3 + x4 + 5 eq w: 1 app^5_if_reach_1 w: x1 + x3 + x5 + 5 app^4_if_reach_1 w: x1 + x3 + 3 false w: 6 app^2_if_reach_1 w: x2 + 1 app^1_if_reach_1 w: x1 + 1 app^2_or w: x2 + 1 app^3_if_reach_1 w: x2 + 1 reach w: 1 if_reach_2 w: 1 app^1_filter2 w: x1 + 1 true w: 6 #app^2_or w: 0 filter2 w: 1 #app^2_union w: 0 0 w: 1 app^3_edge w: x1 + x3 + 4 app^1_edge w: x1 + 2 #app^4_filter2 w: 2 union w: 1 nil w: 2 or w: 1 app^3_if_reach_2 w: 1 #app w: 0 app^4_reach w: x3 + x4 + 1 map w: 1 app^1_filter w: x1 + 3 #app^5_if_reach_1 w: x3 + x4 + x5 + 1 #app^2_eq w: 0 app^2_reach w: 1 app^5_if_reach_2 w: x3 + x5 + 5 cons w: 1 empty w: 1 app^1_or w: x1 + 1 app^2_eq w: x1 + x2 + 3 #app^5_if_reach_2 w: x3 + x4 + x5 filter w: 1 if_reach_1 w: 1 app^3_filter2 w: x1 + x2 + x3 + 3 app^2_filter w: 1 app^2_if_reach_2 w: x1 + x2 + 1 app^2_union w: x1 + x2 + 1 app^1_map w: x1 + 1 app^1_if_reach_2 w: x1 + 1 app^2_cons w: x1 + x2 + 2 app^1_eq w: 1 app^1_s w: 1 app^2_map w: 1 #app^2_filter w: 1 app w: x1 + x2 + 1 USABLE RULES: { 7 8 } Removed DPs: #3 #8 #9 Number of SCCs: 1, DPs: 2 SCC { #6 #12 } POLO(Sum)... succeeded. #app^4_reach w: x3 + 2 s w: 1 app^1_reach w: x1 + 1 app^2_edge w: x1 + x2 + 3 app^1_cons w: x1 + 1 app^1_union w: x1 + 1 #app^2_map w: 0 app^4_if_reach_2 w: x1 + x2 + x3 + 3 app^3_reach w: x1 + x2 + x3 + 3 edge w: 1 app^2_filter2 w: x1 + x2 + 2 app^4_filter2 w: x1 + x3 + x4 + 5 eq w: 1 app^5_if_reach_1 w: x1 + x5 + 5 app^4_if_reach_1 w: x1 + x3 + 3 false w: 6 app^2_if_reach_1 w: x2 + 1 app^1_if_reach_1 w: x1 + 1 app^2_or w: x2 app^3_if_reach_1 w: x2 + 1 reach w: 1 if_reach_2 w: 1 app^1_filter2 w: x1 + 1 true w: 6 #app^2_or w: 0 filter2 w: 1 #app^2_union w: 0 0 w: 1 app^3_edge w: x1 + x3 + 4 app^1_edge w: x1 + 2 #app^4_filter2 w: 2 union w: 1 nil w: 2 or w: 1 app^3_if_reach_2 w: 1 #app w: 0 app^4_reach w: x2 + x4 + 1 map w: 1 app^1_filter w: x1 + 3 #app^5_if_reach_1 w: x4 + 1 #app^2_eq w: 0 app^2_reach w: 1 app^5_if_reach_2 w: x1 + x5 + 5 cons w: 1 empty w: 1 app^1_or w: x1 + 1 app^2_eq w: x1 + x2 + 3 #app^5_if_reach_2 w: 0 filter w: 1 if_reach_1 w: 1 app^3_filter2 w: x1 + x2 + x3 + 3 app^2_filter w: x1 + 1 app^2_if_reach_2 w: x1 + x2 + 1 app^2_union w: x1 + x2 + 1 app^1_map w: x1 + 1 app^1_if_reach_2 w: x1 + 1 app^2_cons w: x1 + x2 + 2 app^1_eq w: 1 app^1_s w: 1 app^2_map w: 1 #app^2_filter w: 1 app w: x1 + x2 + 1 USABLE RULES: { 7 8 } Removed DPs: #6 #12 Number of SCCs: 0, DPs: 0