MAYBE (ignored inputs)COMMENT TPDB SRS_Standard/Zantema_06/05 Rewrite Rules: [ a(a(b(b(?x)))) -> b(b(b(a(a(a(?x)))))), c(?x) -> c(a(?x)), c(?x) -> c(b(?x)) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ c(a(?x_1)) = c(b(?x_1)) ] Overlay, check Innermost Termination... unknown Innermost 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: [ c(b(?x)) = c(a(?x)), c(a(?x)) = c(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 <2, 1> preceded by [] joinable by a reduction of rules <[([],2),([],1),([],1),([(c,1)],0)], [([],1),([],1),([],2),([],2),([],2)]> unknown Diagram Decreasing check Non-Confluence... obtain 7 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... failure(empty P) unknown Reduction-Preserving Completion check by Ordered Rewriting... remove redundants rules and split R-part: [ a(a(b(b(?x)))) -> b(b(b(a(a(a(?x)))))), c(?x) -> c(a(?x)), c(?x) -> c(b(?x)) ] E-part: [ ] ...failed to find a suitable LPO. unknown Confluence by Ordered Rewriting Direct Methods: Can't judge Try Persistent Decomposition for... [ a(a(b(b(?x)))) -> b(b(b(a(a(a(?x)))))), c(?x) -> c(a(?x)), c(?x) -> c(b(?x)) ] Sort Assignment: a : 8=>8 b : 8=>8 c : 8=>10 maximal types: {8,10} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ a(a(b(b(?x)))) -> b(b(b(a(a(a(?x)))))), c(?x) -> c(a(?x)), c(?x) -> c(b(?x)) ] Layer Preserving Decomposition failed: Can't judge Try Commutative Decomposition for... [ a(a(b(b(?x)))) -> b(b(b(a(a(a(?x)))))), c(?x) -> c(a(?x)), c(?x) -> c(b(?x)) ] Outside Critical Pair: by Rules <2, 1> develop reducts from lhs term... <{2}, c(b(b(?x_2)))> <{1}, c(a(b(?x_2)))> <{}, c(b(?x_2))> develop reducts from rhs term... <{2}, c(b(a(?x_2)))> <{1}, c(a(a(?x_2)))> <{}, c(a(?x_2))> Try A Minimal Decomposition {1,2}{0} {1,2} (cm)Rewrite Rules: [ c(?x) -> c(a(?x)), c(?x) -> c(b(?x)) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ c(a(?x)) = c(b(?x)) ] Overlay, check Innermost Termination... unknown Innermost 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: [ c(b(?x)) = c(a(?x)), c(a(?x)) = c(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 <1, 0> preceded by [] unknown Diagram Decreasing check Non-Confluence... obtain 6 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... failure(empty P) unknown Reduction-Preserving Completion check by Ordered Rewriting... remove redundants rules and split R-part: [ c(?x) -> c(a(?x)), c(?x) -> c(b(?x)) ] E-part: [ ] ...failed to find a suitable LPO. unknown Confluence by Ordered Rewriting Direct Methods: Can't judge Try Persistent Decomposition for... [ c(?x) -> c(a(?x)), c(?x) -> c(b(?x)) ] Sort Assignment: a : 5=>5 b : 5=>5 c : 5=>9 maximal types: {5,9} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ c(?x) -> c(a(?x)), c(?x) -> c(b(?x)) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible {0} (cm)Rewrite Rules: [ a(a(b(b(?x)))) -> b(b(b(a(a(a(?x)))))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth & Bendix Linear Development Closed Direct Methods: CR Commutative Decomposition failed: Can't judge No further decomposition possible Combined result: Can't judge 947.trs: Failure(unknown CR) (3368 msec.)