YES
(ignored inputs)COMMENT submitted by: Johannes Waldmann
Rewrite Rules:
[ a(c(?x)) -> a(a(?x)),
b(c(?x)) -> c(b(?x)),
a(c(?x)) -> a(b(?x)),
b(c(?x)) -> a(c(?x)),
c(b(?x)) -> b(c(?x)),
a(b(?x)) -> b(a(?x)),
a(b(?x)) -> c(a(?x)),
a(a(?x)) -> a(c(?x)),
c(a(?x)) -> a(b(?x)) ]
Apply Direct Methods...
Inner CPs:
[ a(b(c(?x_4))) = a(a(b(?x_4))),
a(a(b(?x_8))) = a(a(a(?x_8))),
b(b(c(?x_4))) = c(b(b(?x_4))),
b(a(b(?x_8))) = c(b(a(?x_8))),
a(b(c(?x_4))) = a(b(b(?x_4))),
a(a(b(?x_8))) = a(b(a(?x_8))),
b(b(c(?x_4))) = a(c(b(?x_4))),
b(a(b(?x_8))) = a(c(a(?x_8))),
c(c(b(?x_1))) = b(c(c(?x_1))),
c(a(c(?x_3))) = b(c(c(?x_3))),
a(c(b(?x_1))) = b(a(c(?x_1))),
a(a(c(?x_3))) = b(a(c(?x_3))),
a(c(b(?x_1))) = c(a(c(?x_1))),
a(a(c(?x_3))) = c(a(c(?x_3))),
a(a(a(?x))) = a(c(c(?x))),
a(a(b(?x_2))) = a(c(c(?x_2))),
a(b(a(?x_5))) = a(c(b(?x_5))),
a(c(a(?x_6))) = a(c(b(?x_6))),
c(a(a(?x))) = a(b(c(?x))),
c(a(b(?x_2))) = a(b(c(?x_2))),
c(b(a(?x_5))) = a(b(b(?x_5))),
c(c(a(?x_6))) = a(b(b(?x_6))),
c(a(c(?x_7))) = a(b(a(?x_7))),
a(a(c(?x))) = a(c(a(?x))) ]
Outer CPs:
[ a(a(?x)) = a(b(?x)),
c(b(?x_1)) = a(c(?x_1)),
b(a(?x_5)) = c(a(?x_5)) ]
not Overlay, check Termination...
unknown/not Terminating
unknown Knuth & Bendix
Linear
unknown Development Closed
unknown Strongly Closed
unknown Weakly-Non-Overlapping & Non-Collapsing & Shallow
unknown Upside-Parallel-Closed/Outside-Closed
(inner) Parallel CPs: (not computed)
unknown Toyama (Parallel CPs)
Simultaneous CPs:
[ a(b(?x)) = a(a(?x)),
a(b(c(?x_5))) = a(a(b(?x_5))),
a(a(b(?x_9))) = a(a(a(?x_9))),
a(c(b(c(?x_5)))) = a(a(a(b(?x_5)))),
a(c(a(b(?x_9)))) = a(a(a(a(?x_9)))),
a(b(b(c(?x_5)))) = c(a(a(b(?x_5)))),
a(b(a(b(?x_9)))) = c(a(a(a(?x_9)))),
a(c(c(?x))) = a(a(a(?x))),
a(b(c(?x))) = c(a(a(?x))),
a(c(?x)) = c(b(?x)),
b(b(c(?x_5))) = c(b(b(?x_5))),
b(a(b(?x_9))) = c(b(a(?x_9))),
b(c(b(c(?x_5)))) = c(c(b(b(?x_5)))),
b(c(a(b(?x_9)))) = c(c(b(a(?x_9)))),
b(a(b(c(?x_5)))) = a(c(b(b(?x_5)))),
b(a(a(b(?x_9)))) = a(c(b(a(?x_9)))),
c(a(b(c(?x_5)))) = a(c(b(b(?x_5)))),
c(a(a(b(?x_9)))) = a(c(b(a(?x_9)))),
b(c(c(?x))) = c(c(b(?x))),
b(a(c(?x))) = a(c(b(?x))),
c(a(c(?x))) = a(c(b(?x))),
a(a(?x)) = a(b(?x)),
a(b(c(?x_5))) = a(b(b(?x_5))),
a(a(b(?x_9))) = a(b(a(?x_9))),
a(c(b(c(?x_5)))) = a(a(b(b(?x_5)))),
a(c(a(b(?x_9)))) = a(a(b(a(?x_9)))),
a(b(b(c(?x_5)))) = c(a(b(b(?x_5)))),
a(b(a(b(?x_9)))) = c(a(b(a(?x_9)))),
a(c(c(?x))) = a(a(b(?x))),
a(b(c(?x))) = c(a(b(?x))),
c(b(?x)) = a(c(?x)),
b(b(c(?x_5))) = a(c(b(?x_5))),
b(a(b(?x_9))) = a(c(a(?x_9))),
b(c(b(c(?x_5)))) = c(a(c(b(?x_5)))),
b(c(a(b(?x_9)))) = c(a(c(a(?x_9)))),
b(a(b(c(?x_5)))) = a(a(c(b(?x_5)))),
b(a(a(b(?x_9)))) = a(a(c(a(?x_9)))),
c(a(b(c(?x_5)))) = a(a(c(b(?x_5)))),
c(a(a(b(?x_9)))) = a(a(c(a(?x_9)))),
b(c(c(?x))) = c(a(c(?x))),
b(a(c(?x))) = a(a(c(?x))),
c(a(c(?x))) = a(a(c(?x))),
c(c(b(?x_3))) = b(c(c(?x_3))),
c(a(c(?x_5))) = b(c(c(?x_5))),
a(a(c(b(?x_3)))) = a(b(c(c(?x_3)))),
a(a(a(c(?x_5)))) = a(b(c(c(?x_5)))),
c(b(c(b(?x_3)))) = b(b(c(c(?x_3)))),
c(b(a(c(?x_5)))) = b(b(c(c(?x_5)))),
a(b(c(b(?x_3)))) = a(b(c(c(?x_3)))),
a(b(a(c(?x_5)))) = a(b(c(c(?x_5)))),
a(c(c(b(?x_3)))) = b(b(c(c(?x_3)))),
a(c(a(c(?x_5)))) = b(b(c(c(?x_5)))),
a(a(b(?x))) = a(b(c(?x))),
c(b(b(?x))) = b(b(c(?x))),
a(b(b(?x))) = a(b(c(?x))),
a(c(b(?x))) = b(b(c(?x))),
c(a(?x)) = b(a(?x)),
a(c(b(?x_3))) = b(a(c(?x_3))),
a(a(c(?x_5))) = b(a(c(?x_5))),
a(c(c(b(?x_3)))) = a(b(a(c(?x_3)))),
a(c(a(c(?x_5)))) = a(b(a(c(?x_5)))),
a(b(c(b(?x_3)))) = c(b(a(c(?x_3)))),
a(b(a(c(?x_5)))) = c(b(a(c(?x_5)))),
a(c(b(?x))) = a(b(a(?x))),
a(b(b(?x))) = c(b(a(?x))),
b(a(?x)) = c(a(?x)),
a(c(b(?x_3))) = c(a(c(?x_3))),
a(a(c(?x_5))) = c(a(c(?x_5))),
a(c(c(b(?x_3)))) = a(c(a(c(?x_3)))),
a(c(a(c(?x_5)))) = a(c(a(c(?x_5)))),
a(b(c(b(?x_3)))) = c(c(a(c(?x_3)))),
a(b(a(c(?x_5)))) = c(c(a(c(?x_5)))),
a(c(b(?x))) = a(c(a(?x))),
a(b(b(?x))) = c(c(a(?x))),
a(a(c(?x_1))) = a(c(a(?x_1))),
a(a(a(?x_2))) = a(c(c(?x_2))),
a(a(b(?x_4))) = a(c(c(?x_4))),
a(b(a(?x_7))) = a(c(b(?x_7))),
a(c(a(?x_8))) = a(c(b(?x_8))),
a(c(a(c(?x_1)))) = a(a(c(a(?x_1)))),
a(c(a(a(?x_2)))) = a(a(c(c(?x_2)))),
a(c(a(b(?x_4)))) = a(a(c(c(?x_4)))),
a(c(b(a(?x_7)))) = a(a(c(b(?x_7)))),
a(c(c(a(?x_8)))) = a(a(c(b(?x_8)))),
a(b(a(c(?x_1)))) = c(a(c(a(?x_1)))),
a(b(a(a(?x_2)))) = c(a(c(c(?x_2)))),
a(b(a(b(?x_4)))) = c(a(c(c(?x_4)))),
a(b(b(a(?x_7)))) = c(a(c(b(?x_7)))),
a(b(c(a(?x_8)))) = c(a(c(b(?x_8)))),
a(c(a(?x))) = a(a(c(?x))),
a(b(a(?x))) = c(a(c(?x))),
c(a(a(?x_2))) = a(b(c(?x_2))),
c(a(b(?x_4))) = a(b(c(?x_4))),
c(b(a(?x_7))) = a(b(b(?x_7))),
c(c(a(?x_8))) = a(b(b(?x_8))),
c(a(c(?x_9))) = a(b(a(?x_9))),
a(a(a(a(?x_2)))) = a(a(b(c(?x_2)))),
a(a(a(b(?x_4)))) = a(a(b(c(?x_4)))),
a(a(b(a(?x_7)))) = a(a(b(b(?x_7)))),
a(a(c(a(?x_8)))) = a(a(b(b(?x_8)))),
a(a(a(c(?x_9)))) = a(a(b(a(?x_9)))),
c(b(a(a(?x_2)))) = b(a(b(c(?x_2)))),
c(b(a(b(?x_4)))) = b(a(b(c(?x_4)))),
c(b(b(a(?x_7)))) = b(a(b(b(?x_7)))),
c(b(c(a(?x_8)))) = b(a(b(b(?x_8)))),
c(b(a(c(?x_9)))) = b(a(b(a(?x_9)))),
a(b(a(a(?x_2)))) = a(a(b(c(?x_2)))),
a(b(a(b(?x_4)))) = a(a(b(c(?x_4)))),
a(b(b(a(?x_7)))) = a(a(b(b(?x_7)))),
a(b(c(a(?x_8)))) = a(a(b(b(?x_8)))),
a(b(a(c(?x_9)))) = a(a(b(a(?x_9)))),
a(c(a(a(?x_2)))) = b(a(b(c(?x_2)))),
a(c(a(b(?x_4)))) = b(a(b(c(?x_4)))),
a(c(b(a(?x_7)))) = b(a(b(b(?x_7)))),
a(c(c(a(?x_8)))) = b(a(b(b(?x_8)))),
a(c(a(c(?x_9)))) = b(a(b(a(?x_9)))),
a(a(a(?x))) = a(a(b(?x))),
c(b(a(?x))) = b(a(b(?x))),
a(b(a(?x))) = a(a(b(?x))),
a(c(a(?x))) = b(a(b(?x))) ]
unknown Okui (Simultaneous CPs)
unknown Strongly Depth-Preserving & Root-E-Closed/Non-E-Overlapping
unknown Strongly Weight-Preserving & Root-E-Closed/Non-E-Overlapping
check Locally Decreasing Diagrams by Rule Labelling...
Critical Pair by Rules <4, 0> preceded by [(a,1)]
joinable by a reduction of rules <[([(a,1)],1)], [([],7)]>
Critical Pair by Rules <8, 0> preceded by [(a,1)]
joinable by a reduction of rules <[([(a,1)],6)], [([],7)]>
Critical Pair by Rules <4, 1> preceded by [(b,1)]
joinable by a reduction of rules <[([(b,1)],1)], [([],4)]>
Critical Pair by Rules <8, 1> preceded by [(b,1)]
joinable by a reduction of rules <[([(b,1)],6)], [([],4)]>
Critical Pair by Rules <4, 2> preceded by [(a,1)]
joinable by a reduction of rules <[([(a,1)],1),([],2)], []>
joinable by a reduction of rules <[([],6),([(c,1)],2)], [([],6)]>
joinable by a reduction of rules <[([],5),([(b,1)],2)], [([],5)]>
Critical Pair by Rules <8, 2> preceded by [(a,1)]
joinable by a reduction of rules <[([(a,1)],5)], []>
Critical Pair by Rules <4, 3> preceded by [(b,1)]
joinable by a reduction of rules <[([(b,1)],1),([],3)], []>
joinable by a reduction of rules <[([(b,1)],3)], [([(a,1)],4),([],5)]>
joinable by a reduction of rules <[([(b,1)],3),([(b,1)],2)], [([],2),([],5)]>
Critical Pair by Rules <8, 3> preceded by [(b,1)]
joinable by a reduction of rules <[([(b,1)],6),([],3)], []>
Critical Pair by Rules <1, 4> preceded by [(c,1)]
joinable by a reduction of rules <[([(c,1)],4)], [([],1)]>
Critical Pair by Rules <3, 4> preceded by [(c,1)]
joinable by a reduction of rules <[], [([],1),([(c,1)],3)]>
joinable by a reduction of rules <[([],8)], [([],3),([],2)]>
joinable by a reduction of rules <[([],8),([(a,1)],3)], [([],3),([],0)]>
Critical Pair by Rules <1, 5> preceded by [(a,1)]
joinable by a reduction of rules <[([(a,1)],4),([],5)], []>
joinable by a reduction of rules <[([],2),([],5)], [([(b,1)],2)]>
Critical Pair by Rules <3, 5> preceded by [(a,1)]
joinable by a reduction of rules <[([(a,1)],2),([(a,1)],5),([],5)], [([(b,1)],0)]>
joinable by a reduction of rules <[([],7),([],2),([],5)], []>
joinable by a reduction of rules <[([(a,1)],2),([(a,1)],6)], [([(b,1)],2),([(b,1)],6),([],3)]>
joinable by a reduction of rules <[([(a,1)],0),([],7)], [([(b,1)],2),([(b,1)],6),([],3)]>
Critical Pair by Rules <1, 6> preceded by [(a,1)]
joinable by a reduction of rules <[([(a,1)],4)], [([],8)]>
Critical Pair by Rules <3, 6> preceded by [(a,1)]
joinable by a reduction of rules <[([],7),([],2)], [([],8)]>
joinable by a reduction of rules <[], [([],8),([(a,1)],3)]>
joinable by a reduction of rules <[([(a,1)],2),([(a,1)],5)], [([(c,1)],0),([],8)]>
joinable by a reduction of rules <[([(a,1)],2),([],7)], [([],8),([(a,1)],1)]>
Critical Pair by Rules <0, 7> preceded by [(a,1)]
joinable by a reduction of rules <[([(a,1)],7)], [([],0)]>
Critical Pair by Rules <2, 7> preceded by [(a,1)]
joinable by a reduction of rules <[([],7),([(a,1)],4)], [([],2)]>
joinable by a reduction of rules <[], [([],0),([(a,1)],2)]>
joinable by a reduction of rules <[([],7)], [([],2),([(a,1)],1)]>
joinable by a reduction of rules <[([(a,1)],6),([],0)], [([],0),([(a,1)],0)]>
Critical Pair by Rules <5, 7> preceded by [(a,1)]
joinable by a reduction of rules <[], [([],0),([(a,1)],5)]>
joinable by a reduction of rules <[([],6),([(c,1)],7)], [([(a,1)],4),([],6)]>
joinable by a reduction of rules <[([],5),([(b,1)],7)], [([(a,1)],4),([],5)]>
Critical Pair by Rules <6, 7> preceded by [(a,1)]
joinable by a reduction of rules <[([(a,1)],8)], [([],0)]>
Critical Pair by Rules <0, 8> preceded by [(c,1)]
joinable by a reduction of rules <[([(c,1)],7)], [([],6)]>
Critical Pair by Rules <2, 8> preceded by [(c,1)]
joinable by a reduction of rules <[], [([],6),([(c,1)],2)]>
joinable by a reduction of rules <[([],8)], [([(a,1)],1),([],2)]>
joinable by a reduction of rules <[([],8),([],5)], [([],5),([(b,1)],2)]>
Critical Pair by Rules <5, 8> preceded by [(c,1)]
joinable by a reduction of rules <[([],4),([(b,1)],8)], [([],5)]>
joinable by a reduction of rules <[], [([],6),([(c,1)],5)]>
joinable by a reduction of rules <[([],4)], [([],5),([(b,1)],6)]>
Critical Pair by Rules <6, 8> preceded by [(c,1)]
joinable by a reduction of rules <[([(c,1)],8)], [([],6)]>
Critical Pair by Rules <7, 8> preceded by [(c,1)]
joinable by a reduction of rules <[([(c,1)],0)], [([],6)]>
Critical Pair by Rules <7, 7> preceded by [(a,1)]
joinable by a reduction of rules <[([(a,1)],2)], [([(a,1)],8)]>
joinable by a reduction of rules <[([(a,1)],0)], [([],0)]>
Critical Pair by Rules <2, 0> preceded by []
joinable by a reduction of rules <[], [([],7),([],2)]>
Critical Pair by Rules <3, 1> preceded by []
joinable by a reduction of rules <[], [([],4),([],3)]>
Critical Pair by Rules <6, 5> preceded by []
joinable by a reduction of rules <[([],8),([],5)], []>
unknown Diagram Decreasing
check Non-Confluence...
obtain 14 rules by 3 steps unfolding
obtain 100 candidates for checking non-joinability
check by TCAP-Approximation (failure)
check by Ordering(rpo), check by Tree-Automata Approximation (failure)
check by Interpretation(mod2) (failure)
check by Descendants-Approximation, check by Ordering(poly) (failure)
unknown Non-Confluence
unknown Huet (modulo AC)
check by Reduction-Preserving Completion...
STEP: 1 (parallel)
S:
[ a(c(?x)) -> a(b(?x)),
b(c(?x)) -> a(c(?x)),
a(b(?x)) -> b(a(?x)) ]
P:
[ a(c(?x)) -> a(a(?x)),
b(c(?x)) -> c(b(?x)),
c(b(?x)) -> b(c(?x)),
a(b(?x)) -> c(a(?x)),
a(a(?x)) -> a(c(?x)),
c(a(?x)) -> a(b(?x)) ]
S: terminating
CP(S,S):
--> => no
PCP_in(symP,S):
--> => yes
--> => no
--> => no
--> => yes
--> => yes
CP(S,symP):
--> => yes
--> => no
--> => no
--> => no
--> => no
--> => no
--> => no
--> => no
--> => no
check joinability condition:
check modulo joinability of b(a(a(?x_1))) and b(b(a(?x_1))): joinable by {0}
check modulo joinability of b(a(a(?x_2))) and b(b(a(?x_2))): joinable by {0}
check modulo joinability of b(b(a(?x_4))) and b(a(a(?x_4))): joinable by {0}
check modulo joinability of c(b(a(?x))) and b(a(a(?x))): joinable by {1}
check modulo reachablity from b(a(?x)) to a(a(?x)): maybe not reachable
check modulo joinability of c(b(a(?x))) and b(a(a(?x))): joinable by {1}
check modulo reachablity from b(a(?x)) to c(b(?x)): maybe not reachable
check modulo joinability of b(a(a(?x))) and c(b(a(?x))): joinable by {1}
check modulo joinability of b(a(a(?x))) and b(b(a(?x))): joinable by {0}
check modulo joinability of c(b(a(?x))) and b(b(a(?x))): joinable by {0,1}
check modulo reachablity from b(a(?x)) to c(a(?x)): maybe not reachable
failed
failure(Step 1)
[ a(a(?x)) -> b(a(?x)),
c(b(?x)) -> b(a(?x)),
c(a(?x)) -> b(a(?x)) ]
Added S-Rules:
[ a(a(?x)) -> b(a(?x)),
c(b(?x)) -> b(a(?x)),
c(a(?x)) -> b(a(?x)) ]
Added P-Rules:
[ ]
replace: b(c(?x)) -> a(c(?x)) => b(c(?x)) -> a(a(?x))
replace: a(c(?x)) -> a(b(?x)) => a(c(?x)) -> c(a(?x))
STEP: 2 (linear)
S:
[ a(c(?x)) -> a(b(?x)),
b(c(?x)) -> a(c(?x)),
a(b(?x)) -> b(a(?x)) ]
P:
[ a(c(?x)) -> a(a(?x)),
b(c(?x)) -> c(b(?x)),
c(b(?x)) -> b(c(?x)),
a(b(?x)) -> c(a(?x)),
a(a(?x)) -> a(c(?x)),
c(a(?x)) -> a(b(?x)) ]
S: terminating
CP(S,S):
--> => no
CP_in(symP,S):
--> => no
--> => yes
--> => yes
--> => yes
--> => no
CP(S,symP):
--> => yes
--> => no
--> => no
--> => no
--> => no
--> => no
--> => no
--> => no
--> => no
check joinability condition:
check modulo joinability of b(a(a(?x_1))) and b(b(a(?x_1))): maybe not joinable
check modulo joinability of b(a(a(?x))) and b(b(a(?x))): maybe not joinable
check modulo joinability of b(b(a(?x))) and b(a(a(?x))): maybe not joinable
check modulo joinability of c(b(a(?x))) and b(a(a(?x))): joinable by {0,1}
check modulo reachablity from b(a(?x)) to a(a(?x)): maybe not reachable
check modulo joinability of c(b(a(?x))) and b(a(a(?x))): joinable by {0,1}
check modulo reachablity from b(a(?x)) to c(b(?x)): maybe not reachable
check modulo joinability of b(a(a(?x))) and c(b(a(?x))): joinable by {0,1}
check modulo joinability of b(a(a(?x))) and b(b(a(?x))): maybe not joinable
check modulo joinability of c(b(a(?x))) and b(b(a(?x))): maybe not joinable
check modulo reachablity from b(a(?x)) to c(a(?x)): maybe not reachable
failed
failure(Step 2)
[ a(a(?x)) -> b(a(?x)),
c(b(?x)) -> b(a(?x)),
c(a(?x)) -> b(a(?x)) ]
Added S-Rules:
[ a(a(?x)) -> b(a(?x)),
c(b(?x)) -> b(a(?x)),
c(a(?x)) -> b(a(?x)) ]
Added P-Rules:
[ ]
replace: b(c(?x)) -> a(c(?x)) => b(c(?x)) -> a(a(?x))
replace: a(c(?x)) -> a(b(?x)) => a(c(?x)) -> c(a(?x))
STEP: 3 (relative)
S:
[ a(c(?x)) -> a(b(?x)),
b(c(?x)) -> a(c(?x)),
a(b(?x)) -> b(a(?x)) ]
P:
[ a(c(?x)) -> a(a(?x)),
b(c(?x)) -> c(b(?x)),
c(b(?x)) -> b(c(?x)),
a(b(?x)) -> c(a(?x)),
a(a(?x)) -> a(c(?x)),
c(a(?x)) -> a(b(?x)) ]
Check relative termination:
[ a(c(?x)) -> a(b(?x)),
b(c(?x)) -> a(c(?x)),
a(b(?x)) -> b(a(?x)) ]
[ a(c(?x)) -> a(a(?x)),
b(c(?x)) -> c(b(?x)),
c(b(?x)) -> b(c(?x)),
a(b(?x)) -> c(a(?x)),
a(a(?x)) -> a(c(?x)),
c(a(?x)) -> a(b(?x)) ]
Polynomial Interpretation:
a:= (2)*x1
b:= (1)+(2)*x1
c:= (2)*x1
retract b(c(?x)) -> a(c(?x))
retract a(b(?x)) -> b(a(?x))
retract c(b(?x)) -> b(c(?x))
retract a(b(?x)) -> c(a(?x))
Polynomial Interpretation:
a:= (1)+(2)*x1*x1
b:= (1)*x1
c:= (1)+(2)*x1*x1
relatively terminating
S/P: relatively terminating
check CP condition:
failed
failure(Step 3)
STEP: 4 (parallel)
S:
[ a(c(?x)) -> a(b(?x)),
b(c(?x)) -> a(c(?x)),
a(b(?x)) -> b(a(?x)),
a(a(?x)) -> b(a(?x)),
c(b(?x)) -> b(a(?x)),
c(a(?x)) -> b(a(?x)) ]
P:
[ a(c(?x)) -> a(a(?x)),
b(c(?x)) -> c(b(?x)),
c(b(?x)) -> b(c(?x)),
a(b(?x)) -> c(a(?x)),
a(a(?x)) -> a(c(?x)),
c(a(?x)) -> a(b(?x)) ]
S: terminating
CP(S,S):
--> => yes
--> => yes
--> => yes
--> => yes
--> => yes
--> => yes
--> => yes
--> => yes
--> => yes
--> => yes
--> => yes
--> => yes
PCP_in(symP,S):
--> => yes
--> => yes
--> => yes
--> => yes
--> => yes
--> => yes
--> => yes
--> => yes
--> => yes
--> => yes
--> => yes
--> => yes
CP(S,symP):
--> => yes
--> => yes
--> => yes
--> => yes
--> => yes
--> => yes
--> => yes
--> => yes
--> => yes
--> => yes
--> => yes
--> => yes
--> => yes
--> => yes
--> => yes
--> => yes
--> => yes
--> => yes
S:
[ a(c(?x)) -> a(b(?x)),
b(c(?x)) -> a(c(?x)),
a(b(?x)) -> b(a(?x)),
a(a(?x)) -> b(a(?x)),
c(b(?x)) -> b(a(?x)),
c(a(?x)) -> b(a(?x)) ]
P:
[ a(c(?x)) -> a(a(?x)),
b(c(?x)) -> c(b(?x)),
c(b(?x)) -> b(c(?x)),
a(b(?x)) -> c(a(?x)),
a(a(?x)) -> a(c(?x)),
c(a(?x)) -> a(b(?x)) ]
Success
Reduction-Preserving Completion
Direct Methods: CR
Combined result: CR
1024.trs: Success(CR)
(5430 msec.)