/export/starexec/sandbox2/solver/bin/starexec_run_Default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Input TRS: 1: intersect'ii'in(cons(X,X0),cons(X,X1)) -> intersect'ii'out() 2: intersect'ii'in(Xs,cons(X0,Ys)) -> u'1'1(intersect'ii'in(Xs,Ys)) 3: u'1'1(intersect'ii'out()) -> intersect'ii'out() 4: intersect'ii'in(cons(X0,Xs),Ys) -> u'2'1(intersect'ii'in(Xs,Ys)) 5: u'2'1(intersect'ii'out()) -> intersect'ii'out() 6: reduce'ii'in(sequent(cons(if(A,B),Fs),Gs),NF) -> u'3'1(reduce'ii'in(sequent(cons(x'2b(x'2d(B),A),Fs),Gs),NF)) 7: u'3'1(reduce'ii'out()) -> reduce'ii'out() 8: reduce'ii'in(sequent(cons(iff(A,B),Fs),Gs),NF) -> u'4'1(reduce'ii'in(sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs),NF)) 9: u'4'1(reduce'ii'out()) -> reduce'ii'out() 10: reduce'ii'in(sequent(cons(x'2a(F1,F2),Fs),Gs),NF) -> u'5'1(reduce'ii'in(sequent(cons(F1,cons(F2,Fs)),Gs),NF)) 11: u'5'1(reduce'ii'out()) -> reduce'ii'out() 12: reduce'ii'in(sequent(cons(x'2b(F1,F2),Fs),Gs),NF) -> u'6'1(reduce'ii'in(sequent(cons(F1,Fs),Gs),NF),F2,Fs,Gs,NF) 13: u'6'1(reduce'ii'out(),F2,Fs,Gs,NF) -> u'6'2(reduce'ii'in(sequent(cons(F2,Fs),Gs),NF)) 14: u'6'2(reduce'ii'out()) -> reduce'ii'out() 15: reduce'ii'in(sequent(cons(x'2d(F1),Fs),Gs),NF) -> u'7'1(reduce'ii'in(sequent(Fs,cons(F1,Gs)),NF)) 16: u'7'1(reduce'ii'out()) -> reduce'ii'out() 17: reduce'ii'in(sequent(Fs,cons(if(A,B),Gs)),NF) -> u'8'1(reduce'ii'in(sequent(Fs,cons(x'2b(x'2d(B),A),Gs)),NF)) 18: u'8'1(reduce'ii'out()) -> reduce'ii'out() 19: reduce'ii'in(sequent(Fs,cons(iff(A,B),Gs)),NF) -> u'9'1(reduce'ii'in(sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs)),NF)) 20: u'9'1(reduce'ii'out()) -> reduce'ii'out() 21: reduce'ii'in(sequent(cons(p(V),Fs),Gs),sequent(Left,Right)) -> u'10'1(reduce'ii'in(sequent(Fs,Gs),sequent(cons(p(V),Left),Right))) 22: u'10'1(reduce'ii'out()) -> reduce'ii'out() 23: reduce'ii'in(sequent(Fs,cons(x'2b(G1,G2),Gs)),NF) -> u'11'1(reduce'ii'in(sequent(Fs,cons(G1,cons(G2,Gs))),NF)) 24: u'11'1(reduce'ii'out()) -> reduce'ii'out() 25: reduce'ii'in(sequent(Fs,cons(x'2a(G1,G2),Gs)),NF) -> u'12'1(reduce'ii'in(sequent(Fs,cons(G1,Gs)),NF),Fs,G2,Gs,NF) 26: u'12'1(reduce'ii'out(),Fs,G2,Gs,NF) -> u'12'2(reduce'ii'in(sequent(Fs,cons(G2,Gs)),NF)) 27: u'12'2(reduce'ii'out()) -> reduce'ii'out() 28: reduce'ii'in(sequent(Fs,cons(x'2d(G1),Gs)),NF) -> u'13'1(reduce'ii'in(sequent(cons(G1,Fs),Gs),NF)) 29: u'13'1(reduce'ii'out()) -> reduce'ii'out() 30: reduce'ii'in(sequent(nil(),cons(p(V),Gs)),sequent(Left,Right)) -> u'14'1(reduce'ii'in(sequent(nil(),Gs),sequent(Left,cons(p(V),Right)))) 31: u'14'1(reduce'ii'out()) -> reduce'ii'out() 32: reduce'ii'in(sequent(nil(),nil()),sequent(F1,F2)) -> u'15'1(intersect'ii'in(F1,F2)) 33: u'15'1(intersect'ii'out()) -> reduce'ii'out() 34: tautology'i'in(F) -> u'16'1(reduce'ii'in(sequent(nil(),cons(F,nil())),sequent(nil(),nil()))) 35: u'16'1(reduce'ii'out()) -> tautology'i'out() Number of strict rules: 35 Direct POLO(bPol) ... failed. Uncurrying reduce'ii'in 1: intersect'ii'in(cons(X,X0),cons(X,X1)) -> intersect'ii'out() 2: intersect'ii'in(Xs,cons(X0,Ys)) -> u'1'1(intersect'ii'in(Xs,Ys)) 3: u'1'1(intersect'ii'out()) -> intersect'ii'out() 4: intersect'ii'in(cons(X0,Xs),Ys) -> u'2'1(intersect'ii'in(Xs,Ys)) 5: u'2'1(intersect'ii'out()) -> intersect'ii'out() 6: reduce'ii'in^1_sequent(cons(if(A,B),Fs),Gs,NF) -> u'3'1(reduce'ii'in^1_sequent(cons(x'2b(x'2d(B),A),Fs),Gs,NF)) 7: u'3'1(reduce'ii'out()) -> reduce'ii'out() 8: reduce'ii'in^1_sequent(cons(iff(A,B),Fs),Gs,NF) -> u'4'1(reduce'ii'in^1_sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs,NF)) 9: u'4'1(reduce'ii'out()) -> reduce'ii'out() 10: reduce'ii'in^1_sequent(cons(x'2a(F1,F2),Fs),Gs,NF) -> u'5'1(reduce'ii'in^1_sequent(cons(F1,cons(F2,Fs)),Gs,NF)) 11: u'5'1(reduce'ii'out()) -> reduce'ii'out() 12: reduce'ii'in^1_sequent(cons(x'2b(F1,F2),Fs),Gs,NF) -> u'6'1(reduce'ii'in^1_sequent(cons(F1,Fs),Gs,NF),F2,Fs,Gs,NF) 13: u'6'1(reduce'ii'out(),F2,Fs,Gs,NF) -> u'6'2(reduce'ii'in^1_sequent(cons(F2,Fs),Gs,NF)) 14: u'6'2(reduce'ii'out()) -> reduce'ii'out() 15: reduce'ii'in^1_sequent(cons(x'2d(F1),Fs),Gs,NF) -> u'7'1(reduce'ii'in^1_sequent(Fs,cons(F1,Gs),NF)) 16: u'7'1(reduce'ii'out()) -> reduce'ii'out() 17: reduce'ii'in^1_sequent(Fs,cons(if(A,B),Gs),NF) -> u'8'1(reduce'ii'in^1_sequent(Fs,cons(x'2b(x'2d(B),A),Gs),NF)) 18: u'8'1(reduce'ii'out()) -> reduce'ii'out() 19: reduce'ii'in^1_sequent(Fs,cons(iff(A,B),Gs),NF) -> u'9'1(reduce'ii'in^1_sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs),NF)) 20: u'9'1(reduce'ii'out()) -> reduce'ii'out() 21: reduce'ii'in^1_sequent(cons(p(V),Fs),Gs,sequent(Left,Right)) -> u'10'1(reduce'ii'in^1_sequent(Fs,Gs,sequent(cons(p(V),Left),Right))) 22: u'10'1(reduce'ii'out()) -> reduce'ii'out() 23: reduce'ii'in^1_sequent(Fs,cons(x'2b(G1,G2),Gs),NF) -> u'11'1(reduce'ii'in^1_sequent(Fs,cons(G1,cons(G2,Gs)),NF)) 24: u'11'1(reduce'ii'out()) -> reduce'ii'out() 25: reduce'ii'in^1_sequent(Fs,cons(x'2a(G1,G2),Gs),NF) -> u'12'1(reduce'ii'in^1_sequent(Fs,cons(G1,Gs),NF),Fs,G2,Gs,NF) 26: u'12'1(reduce'ii'out(),Fs,G2,Gs,NF) -> u'12'2(reduce'ii'in^1_sequent(Fs,cons(G2,Gs),NF)) 27: u'12'2(reduce'ii'out()) -> reduce'ii'out() 28: reduce'ii'in^1_sequent(Fs,cons(x'2d(G1),Gs),NF) -> u'13'1(reduce'ii'in^1_sequent(cons(G1,Fs),Gs,NF)) 29: u'13'1(reduce'ii'out()) -> reduce'ii'out() 30: reduce'ii'in^1_sequent(nil(),cons(p(V),Gs),sequent(Left,Right)) -> u'14'1(reduce'ii'in^1_sequent(nil(),Gs,sequent(Left,cons(p(V),Right)))) 31: u'14'1(reduce'ii'out()) -> reduce'ii'out() 32: reduce'ii'in^1_sequent(nil(),nil(),sequent(F1,F2)) -> u'15'1(intersect'ii'in(F1,F2)) 33: u'15'1(intersect'ii'out()) -> reduce'ii'out() 34: tautology'i'in(F) -> u'16'1(reduce'ii'in^1_sequent(nil(),cons(F,nil()),sequent(nil(),nil()))) 35: u'16'1(reduce'ii'out()) -> tautology'i'out() 36: reduce'ii'in(sequent(_1,_2),_3) ->= reduce'ii'in^1_sequent(_1,_2,_3) Number of strict rules: 35 Direct POLO(bPol) ... failed. Dependency Pairs: #1: #intersect'ii'in(Xs,cons(X0,Ys)) -> #u'1'1(intersect'ii'in(Xs,Ys)) #2: #intersect'ii'in(Xs,cons(X0,Ys)) -> #intersect'ii'in(Xs,Ys) #3: #reduce'ii'in^1_sequent(cons(if(A,B),Fs),Gs,NF) -> #u'3'1(reduce'ii'in^1_sequent(cons(x'2b(x'2d(B),A),Fs),Gs,NF)) #4: #reduce'ii'in^1_sequent(cons(if(A,B),Fs),Gs,NF) -> #reduce'ii'in^1_sequent(cons(x'2b(x'2d(B),A),Fs),Gs,NF) #5: #u'6'1(reduce'ii'out(),F2,Fs,Gs,NF) -> #u'6'2(reduce'ii'in^1_sequent(cons(F2,Fs),Gs,NF)) #6: #u'6'1(reduce'ii'out(),F2,Fs,Gs,NF) -> #reduce'ii'in^1_sequent(cons(F2,Fs),Gs,NF) #7: #reduce'ii'in^1_sequent(Fs,cons(x'2b(G1,G2),Gs),NF) -> #u'11'1(reduce'ii'in^1_sequent(Fs,cons(G1,cons(G2,Gs)),NF)) #8: #reduce'ii'in^1_sequent(Fs,cons(x'2b(G1,G2),Gs),NF) -> #reduce'ii'in^1_sequent(Fs,cons(G1,cons(G2,Gs)),NF) #9: #reduce'ii'in^1_sequent(cons(x'2b(F1,F2),Fs),Gs,NF) -> #u'6'1(reduce'ii'in^1_sequent(cons(F1,Fs),Gs,NF),F2,Fs,Gs,NF) #10: #reduce'ii'in^1_sequent(cons(x'2b(F1,F2),Fs),Gs,NF) -> #reduce'ii'in^1_sequent(cons(F1,Fs),Gs,NF) #11: #reduce'ii'in^1_sequent(nil(),cons(p(V),Gs),sequent(Left,Right)) -> #u'14'1(reduce'ii'in^1_sequent(nil(),Gs,sequent(Left,cons(p(V),Right)))) #12: #reduce'ii'in^1_sequent(nil(),cons(p(V),Gs),sequent(Left,Right)) -> #reduce'ii'in^1_sequent(nil(),Gs,sequent(Left,cons(p(V),Right))) #13: #reduce'ii'in^1_sequent(Fs,cons(x'2a(G1,G2),Gs),NF) -> #u'12'1(reduce'ii'in^1_sequent(Fs,cons(G1,Gs),NF),Fs,G2,Gs,NF) #14: #reduce'ii'in^1_sequent(Fs,cons(x'2a(G1,G2),Gs),NF) -> #reduce'ii'in^1_sequent(Fs,cons(G1,Gs),NF) #15: #reduce'ii'in^1_sequent(cons(x'2a(F1,F2),Fs),Gs,NF) -> #u'5'1(reduce'ii'in^1_sequent(cons(F1,cons(F2,Fs)),Gs,NF)) #16: #reduce'ii'in^1_sequent(cons(x'2a(F1,F2),Fs),Gs,NF) -> #reduce'ii'in^1_sequent(cons(F1,cons(F2,Fs)),Gs,NF) #17: #reduce'ii'in^1_sequent(Fs,cons(x'2d(G1),Gs),NF) -> #u'13'1(reduce'ii'in^1_sequent(cons(G1,Fs),Gs,NF)) #18: #reduce'ii'in^1_sequent(Fs,cons(x'2d(G1),Gs),NF) -> #reduce'ii'in^1_sequent(cons(G1,Fs),Gs,NF) #19: #tautology'i'in(F) -> #u'16'1(reduce'ii'in^1_sequent(nil(),cons(F,nil()),sequent(nil(),nil()))) #20: #tautology'i'in(F) -> #reduce'ii'in^1_sequent(nil(),cons(F,nil()),sequent(nil(),nil())) #21: #reduce'ii'in^1_sequent(Fs,cons(if(A,B),Gs),NF) -> #u'8'1(reduce'ii'in^1_sequent(Fs,cons(x'2b(x'2d(B),A),Gs),NF)) #22: #reduce'ii'in^1_sequent(Fs,cons(if(A,B),Gs),NF) -> #reduce'ii'in^1_sequent(Fs,cons(x'2b(x'2d(B),A),Gs),NF) #23: #reduce'ii'in^1_sequent(Fs,cons(iff(A,B),Gs),NF) -> #u'9'1(reduce'ii'in^1_sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs),NF)) #24: #reduce'ii'in^1_sequent(Fs,cons(iff(A,B),Gs),NF) -> #reduce'ii'in^1_sequent(Fs,cons(x'2a(if(A,B),if(B,A)),Gs),NF) #25: #reduce'ii'in^1_sequent(nil(),nil(),sequent(F1,F2)) -> #u'15'1(intersect'ii'in(F1,F2)) #26: #reduce'ii'in^1_sequent(nil(),nil(),sequent(F1,F2)) -> #intersect'ii'in(F1,F2) #27: #u'12'1(reduce'ii'out(),Fs,G2,Gs,NF) -> #u'12'2(reduce'ii'in^1_sequent(Fs,cons(G2,Gs),NF)) #28: #u'12'1(reduce'ii'out(),Fs,G2,Gs,NF) -> #reduce'ii'in^1_sequent(Fs,cons(G2,Gs),NF) #29: #reduce'ii'in(sequent(_1,_2),_3) ->? #reduce'ii'in^1_sequent(_1,_2,_3) #30: #reduce'ii'in^1_sequent(cons(p(V),Fs),Gs,sequent(Left,Right)) -> #u'10'1(reduce'ii'in^1_sequent(Fs,Gs,sequent(cons(p(V),Left),Right))) #31: #reduce'ii'in^1_sequent(cons(p(V),Fs),Gs,sequent(Left,Right)) -> #reduce'ii'in^1_sequent(Fs,Gs,sequent(cons(p(V),Left),Right)) #32: #reduce'ii'in^1_sequent(cons(iff(A,B),Fs),Gs,NF) -> #u'4'1(reduce'ii'in^1_sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs,NF)) #33: #reduce'ii'in^1_sequent(cons(iff(A,B),Fs),Gs,NF) -> #reduce'ii'in^1_sequent(cons(x'2a(if(A,B),if(B,A)),Fs),Gs,NF) #34: #reduce'ii'in^1_sequent(cons(x'2d(F1),Fs),Gs,NF) -> #u'7'1(reduce'ii'in^1_sequent(Fs,cons(F1,Gs),NF)) #35: #reduce'ii'in^1_sequent(cons(x'2d(F1),Fs),Gs,NF) -> #reduce'ii'in^1_sequent(Fs,cons(F1,Gs),NF) #36: #intersect'ii'in(cons(X0,Xs),Ys) -> #u'2'1(intersect'ii'in(Xs,Ys)) #37: #intersect'ii'in(cons(X0,Xs),Ys) -> #intersect'ii'in(Xs,Ys) Number of SCCs: 2, DPs: 18 SCC { #2 #37 } POLO(Sum)... succeeded. iff w: 0 tautology'i'in w: 0 #u'7'1 w: 0 u'12'1 w: 0 x'2d w: 0 #u'12'1 w: 0 #reduce'ii'in w: 0 #u'5'1 w: 0 #u'1'1 w: 0 reduce'ii'in w: 0 u'7'1 w: 0 x'2b w: 0 u'5'1 w: 0 u'6'2 w: 0 u'8'1 w: 0 u'12'2 w: 0 #u'13'1 w: 0 reduce'ii'in^1_sequent w: 0 #u'16'1 w: 0 intersect'ii'out w: 0 intersect'ii'in w: 0 #u'9'1 w: 0 u'6'1 w: 0 #u'14'1 w: 0 p w: 0 u'10'1 w: 0 if w: 0 #u'2'1 w: 0 nil w: 0 #intersect'ii'in w: x1 + x2 u'4'1 w: 0 #u'6'1 w: 0 u'2'1 w: 0 u'9'1 w: 0 #u'11'1 w: 0 tautology'i'out w: 0 #u'15'1 w: 0 u'15'1 w: 0 cons w: x2 + 1 u'13'1 w: 0 reduce'ii'out w: 0 #u'12'2 w: 0 x'2a w: 0 u'14'1 w: 0 #tautology'i'in w: 0 #u'4'1 w: 0 u'3'1 w: 0 #u'8'1 w: 0 sequent w: 0 #u'6'2 w: 0 u'11'1 w: 0 #u'3'1 w: 0 u'1'1 w: 0 #u'10'1 w: 0 u'16'1 w: 0 #reduce'ii'in^1_sequent w: 0 USABLE RULES: { } Removed DPs: #2 #37 Number of SCCs: 1, DPs: 16 SCC { #4 #6 #8..10 #12..14 #16 #18 #22 #24 #28 #31 #33 #35 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... succeeded. iff w: [1,1;1,1] * x1 + [1,1;1,1] * x2 + [1;12] tautology'i'in w: [0;0] #u'7'1 w: [0;0] u'12'1 w: [1,0;0,0] * x4 + [0,1;0,0] * x5 x'2d w: [0,1;1,0] * x1 + [1;1] #u'12'1 w: [1,1;0,0] * x2 + [1,1;0,0] * x3 + [1,1;0,0] * x4 + [1,1;0,0] * x5 + [2;0] #reduce'ii'in w: [0;0] #u'5'1 w: [0;0] #u'1'1 w: [0;0] reduce'ii'in w: [0;0] u'7'1 w: [0;0] x'2b w: [0,0;1,1] * x1 + [0,0;1,1] * x2 + [1;1] u'5'1 w: [0,1;0,0] * x1 u'6'2 w: x1 u'8'1 w: [0;0] u'12'2 w: [0;0] #u'13'1 w: [0;0] reduce'ii'in^1_sequent w: [1,0;0,0] * x2 + [0,1;0,1] * x3 + [1;1] #u'16'1 w: [0;0] intersect'ii'out w: [1;1] intersect'ii'in w: [1,1;1,1] * x1 + [0,0;0,1] * x2 + [1;1] #u'9'1 w: [0;0] u'6'1 w: [1,0;0,0] * x4 + [0,1;0,1] * x5 + [1;1] #u'14'1 w: [0;0] p w: [1,0;1,0] * x1 + [1;1] u'10'1 w: [0;0] if w: [1,1;0,0] * x1 + [0,0;1,1] * x2 + [5;0] #u'2'1 w: [0;0] nil w: [1;0] #intersect'ii'in w: [0;0] u'4'1 w: [0;0] #u'6'1 w: [1,1;0,0] * x2 + [1,1;0,0] * x3 + [1,1;0,0] * x4 + [1,1;0,0] * x5 + [2;0] u'2'1 w: [0,0;0,1] * x1 + [1;0] u'9'1 w: [0,0;0,1] * x1 #u'11'1 w: [0;0] tautology'i'out w: [0;0] #u'15'1 w: [0;0] u'15'1 w: [1,1;1,1] * x1 cons w: [0,1;1,0] * x1 + [1,1;0,0] * x2 + [0;1] u'13'1 w: [0,0;0,1] * x1 + [2;0] reduce'ii'out w: [0;0] #u'12'2 w: [0;0] x'2a w: [0,1;1,0] * x1 + [0,0;1,1] * x2 + [1;1] u'14'1 w: [0;0] #tautology'i'in w: [0;0] #u'4'1 w: [0;0] u'3'1 w: [0;0] #u'8'1 w: [0;0] sequent w: [0,0;1,1] * x1 + [0,0;0,1] * x2 + [1;1] #u'6'2 w: [0;0] u'11'1 w: [0;0] #u'3'1 w: [0;0] u'1'1 w: [0,0;1,0] * x1 + [1;0] #u'10'1 w: [0;0] u'16'1 w: [0;0] #reduce'ii'in^1_sequent w: [1,1;0,0] * x1 + [1,1;0,0] * x2 + [1,1;0,0] * x3 USABLE RULES: { 1..31 33 } Removed DPs: #4 #6 #8..10 #12..14 #16 #18 #22 #24 #28 #33 #35 Number of SCCs: 1, DPs: 1 SCC { #31 } POLO(Sum)... succeeded. iff w: 11 tautology'i'in w: 0 #u'7'1 w: 0 u'12'1 w: x5 + 1 x'2d w: 1 #u'12'1 w: 2 #reduce'ii'in w: 0 #u'5'1 w: 0 #u'1'1 w: 0 reduce'ii'in w: 0 u'7'1 w: 2 x'2b w: 2 u'5'1 w: 0 u'6'2 w: x1 + 2 u'8'1 w: 4 u'12'2 w: 1 #u'13'1 w: 0 reduce'ii'in^1_sequent w: x3 + 1 #u'16'1 w: 0 intersect'ii'out w: 1 intersect'ii'in w: x1 + 1 #u'9'1 w: 0 u'6'1 w: x3 + 2 #u'14'1 w: 0 p w: 1 u'10'1 w: 3 if w: x1 + 4 #u'2'1 w: 0 nil w: 0 #intersect'ii'in w: 0 u'4'1 w: 2 #u'6'1 w: 0 u'2'1 w: 1 u'9'1 w: 0 #u'11'1 w: 0 tautology'i'out w: 0 #u'15'1 w: 0 u'15'1 w: 3 cons w: x2 + 1 u'13'1 w: 2 reduce'ii'out w: 4 #u'12'2 w: 0 x'2a w: x2 + 1 u'14'1 w: 3 #tautology'i'in w: 0 #u'4'1 w: 0 u'3'1 w: 2 #u'8'1 w: 0 sequent w: x1 + x2 + 1 #u'6'2 w: 0 u'11'1 w: 2 #u'3'1 w: 0 u'1'1 w: 1 #u'10'1 w: 0 u'16'1 w: 0 #reduce'ii'in^1_sequent w: x1 + 2 USABLE RULES: { 1..5 18 } Removed DPs: #31 Number of SCCs: 0, DPs: 0