20.039/20.039 NO 20.039/20.039 20.039/20.039 Problem 1: 20.039/20.039 20.039/20.039 20.039/20.039 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.039/20.039 Confluence Problem: 20.039/20.039 (VAR vNonEmpty:S x:S) 20.039/20.039 (STRATEGY CONTEXTSENSITIVE 20.039/20.039 (a) 20.039/20.039 (f 1) 20.039/20.039 (c) 20.039/20.039 (d) 20.039/20.039 (fSNonEmpty) 20.039/20.039 ) 20.039/20.039 (RULES 20.039/20.039 a -> c 20.039/20.039 a -> d 20.039/20.039 f(x:S) -> x:S | x:S ->* c, d ->* x:S 20.039/20.039 ) 20.039/20.039 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.039/20.039 20.039/20.039 20.039/20.039 Problem 1: 20.039/20.039 20.039/20.039 Inlining of Conditions Processor [STERN17]: 20.039/20.039 20.039/20.039 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.039/20.039 Confluence Problem: 20.039/20.039 (VAR vNonEmpty:S x:S) 20.039/20.039 (STRATEGY CONTEXTSENSITIVE 20.039/20.039 (a) 20.039/20.039 (f 1) 20.039/20.039 (c) 20.039/20.039 (d) 20.039/20.039 (fSNonEmpty) 20.039/20.039 ) 20.039/20.039 (RULES 20.039/20.039 a -> c 20.039/20.039 a -> d 20.039/20.039 f(x:S) -> x:S | d ->* x:S, x:S ->* c 20.039/20.039 ) 20.039/20.039 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.039/20.039 20.039/20.039 20.039/20.039 Problem 1: 20.039/20.039 20.039/20.039 Clean CTRS Processor: 20.039/20.039 20.039/20.039 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.039/20.039 Confluence Problem: 20.039/20.039 (STRATEGY CONTEXTSENSITIVE 20.039/20.039 (a) 20.039/20.039 (f 1) 20.039/20.039 (c) 20.039/20.039 (d) 20.039/20.039 (fSNonEmpty) 20.039/20.039 ) 20.039/20.039 (RULES 20.039/20.039 a -> c 20.039/20.039 a -> d 20.039/20.039 ) 20.039/20.039 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.039/20.039 20.039/20.039 CRule InfChecker Info: 20.039/20.039 a -> c 20.039/20.039 Rule remains 20.039/20.039 Proof: 20.039/20.039 NO_CONDS 20.039/20.039 20.039/20.039 CRule InfChecker Info: 20.039/20.039 a -> d 20.039/20.039 Rule remains 20.039/20.039 Proof: 20.039/20.039 NO_CONDS 20.039/20.039 20.039/20.039 CRule InfChecker Info: 20.039/20.039 f(x:S) -> x:S | d ->* x:S, x:S ->* c 20.039/20.039 Rule deleted 20.039/20.039 Proof: 20.039/20.039 YES 20.039/20.039 20.039/20.039 Problem 1: 20.039/20.039 20.039/20.039 Infeasibility Problem: 20.039/20.039 [(VAR vNonEmpty:S vNonEmpty:S:S x:S:S) 20.039/20.039 (STRATEGY CONTEXTSENSITIVE 20.039/20.039 (a) 20.039/20.039 (f 1) 20.039/20.039 (c) 20.039/20.039 (d) 20.039/20.039 (fSNonEmpty) 20.039/20.039 ) 20.039/20.039 (RULES 20.039/20.039 a -> c 20.039/20.039 a -> d 20.039/20.039 f(x:S:S) -> x:S:S | d ->* x:S:S, x:S:S ->* c 20.039/20.039 )] 20.039/20.039 20.039/20.039 Infeasibility Conditions: 20.039/20.039 d ->* x:S:S, x:S:S ->* c 20.039/20.039 20.039/20.039 Problem 1: 20.039/20.039 20.039/20.039 Obtaining a model using Mace4: 20.039/20.039 20.039/20.039 -> Usable Rules: 20.039/20.039 a -> c 20.039/20.039 a -> d 20.039/20.039 f(x:S:S) -> x:S:S | d ->* x:S:S, x:S:S ->* c 20.039/20.039 20.039/20.039 -> Mace4 Output: 20.039/20.039 ============================== Mace4 ================================= 20.039/20.039 Mace4 (64) version 2009-11A, November 2009. 20.039/20.039 Process 48382 was started by ubuntu on ubuntu, 20.039/20.039 Wed Jul 14 10:47:27 2021 20.039/20.039 The command was "./mace4 -c -f /tmp/mace448370-2.in". 20.039/20.039 ============================== end of head =========================== 20.039/20.039 20.039/20.039 ============================== INPUT ================================= 20.039/20.039 20.039/20.039 % Reading from file /tmp/mace448370-2.in 20.039/20.039 20.039/20.039 assign(max_seconds,20). 20.039/20.039 20.039/20.039 formulas(assumptions). 20.039/20.039 ->(x1,y) -> ->(f(x1),f(y)) # label(congruence). 20.039/20.039 ->(a,c) # label(replacement). 20.039/20.039 ->(a,d) # label(replacement). 20.039/20.039 ->*(d,x2) & ->*(x2,c) -> ->(f(x2),x2) # label(replacement). 20.039/20.039 ->*(x,x) # label(reflexivity). 20.039/20.039 ->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity). 20.039/20.039 end_of_list. 20.039/20.039 20.039/20.039 formulas(goals). 20.039/20.039 (exists x2 (->*(d,x2) & ->*(x2,c))) # label(goal). 20.039/20.039 end_of_list. 20.039/20.039 20.039/20.039 ============================== end of input ========================== 20.039/20.039 20.039/20.039 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 20.039/20.039 20.039/20.039 % Formulas that are not ordinary clauses: 20.039/20.039 1 ->(x1,y) -> ->(f(x1),f(y)) # label(congruence) # label(non_clause). [assumption]. 20.039/20.039 2 ->*(d,x2) & ->*(x2,c) -> ->(f(x2),x2) # label(replacement) # label(non_clause). [assumption]. 20.039/20.039 3 ->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity) # label(non_clause). [assumption]. 20.039/20.039 4 (exists x2 (->*(d,x2) & ->*(x2,c))) # label(goal) # label(non_clause) # label(goal). [goal]. 20.039/20.039 20.039/20.039 ============================== end of process non-clausal formulas === 20.039/20.039 20.039/20.039 ============================== CLAUSES FOR SEARCH ==================== 20.039/20.039 20.039/20.039 formulas(mace4_clauses). 20.039/20.039 -->(x,y) | ->(f(x),f(y)) # label(congruence). 20.039/20.039 ->(a,c) # label(replacement). 20.039/20.039 ->(a,d) # label(replacement). 20.039/20.039 -->*(d,x) | -->*(x,c) | ->(f(x),x) # label(replacement). 20.039/20.039 ->*(x,x) # label(reflexivity). 20.039/20.039 -->(x,y) | -->*(y,z) | ->*(x,z) # label(transitivity). 20.039/20.039 -->*(d,x) | -->*(x,c) # label(goal). 20.039/20.039 end_of_list. 20.039/20.039 20.039/20.039 ============================== end of clauses for search ============= 20.039/20.039 20.039/20.039 % There are no natural numbers in the input. 20.039/20.039 20.039/20.039 ============================== DOMAIN SIZE 2 ========================= 20.039/20.039 20.039/20.039 ============================== MODEL ================================= 20.039/20.039 20.039/20.039 interpretation( 2, [number=1, seconds=0], [ 20.039/20.039 20.039/20.039 function(a, [ 0 ]), 20.039/20.039 20.039/20.039 function(c, [ 0 ]), 20.039/20.039 20.039/20.039 function(d, [ 1 ]), 20.039/20.039 20.039/20.039 function(f(_), [ 0, 0 ]), 20.039/20.039 20.039/20.039 relation(->*(_,_), [ 20.039/20.039 1, 1, 20.039/20.039 0, 1 ]), 20.039/20.039 20.039/20.039 relation(->(_,_), [ 20.039/20.039 1, 1, 20.039/20.039 0, 0 ]) 20.039/20.039 ]). 20.039/20.039 20.039/20.039 ============================== end of model ========================== 20.039/20.039 20.039/20.039 ============================== STATISTICS ============================ 20.039/20.039 20.039/20.039 For domain size 2. 20.039/20.039 20.039/20.039 Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds). 20.039/20.039 Ground clauses: seen=20, kept=16. 20.039/20.039 Selections=5, assignments=5, propagations=8, current_models=1. 20.039/20.039 Rewrite_terms=22, rewrite_bools=26, indexes=4. 20.039/20.039 Rules_from_neg_clauses=1, cross_offs=1. 20.039/20.039 20.039/20.039 ============================== end of statistics ===================== 20.039/20.039 20.039/20.039 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 20.039/20.039 20.039/20.039 Exiting with 1 model. 20.039/20.039 20.039/20.039 Process 48382 exit (max_models) Wed Jul 14 10:47:27 2021 20.039/20.039 The process finished Wed Jul 14 10:47:27 2021 20.039/20.039 20.039/20.039 20.039/20.039 Mace4 cooked interpretation: 20.039/20.039 20.039/20.039 20.039/20.039 20.039/20.039 The problem is infeasible. 20.039/20.039 20.039/20.039 20.039/20.039 Problem 1: 20.039/20.039 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.039/20.039 Confluence Problem: 20.039/20.039 (STRATEGY CONTEXTSENSITIVE 20.039/20.039 (a) 20.039/20.039 (f 1) 20.039/20.039 (c) 20.039/20.039 (d) 20.039/20.039 (fSNonEmpty) 20.039/20.039 ) 20.039/20.039 (RULES 20.039/20.039 a -> c 20.039/20.039 a -> d 20.039/20.039 ) 20.039/20.039 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.039/20.039 20.039/20.039 Critical Pairs Processor: 20.039/20.039 -> Rules: 20.039/20.039 a -> c 20.039/20.039 a -> d 20.039/20.039 -> Vars: 20.039/20.039 20.039/20.039 -> FVars: 20.039/20.039 20.039/20.039 -> PVars: 20.039/20.039 20.039/20.039 20.039/20.039 -> Rlps: 20.039/20.039 crule: a -> c, id: 1, possubterms: a-> [] 20.039/20.039 crule: a -> d, id: 2, possubterms: a-> [] 20.039/20.039 20.039/20.039 -> Unifications: 20.039/20.039 R2 unifies with R1 at p: [], l: a, lp: a, conds: {}, sig: {}, l': a, r: d, r': c 20.039/20.039 20.039/20.039 -> Critical pairs info: 20.039/20.039 => Not trivial, Overlay, N1 20.039/20.039 20.039/20.039 -> Problem conclusions: 20.039/20.039 Left linear, Right linear, Linear 20.039/20.039 Not weakly orthogonal, Not almost orthogonal, Not orthogonal 20.039/20.039 CTRS Type: 1 20.039/20.039 Deterministic, Strongly deterministic 20.039/20.039 Oriented CTRS, Properly oriented CTRS, Join CTRS 20.039/20.039 Maybe right-stable CTRS, Overlay CTRS 20.039/20.039 Normal CTRS, Almost normal CTRS 20.039/20.039 Maybe terminating CTRS, Maybe joinable CCPs 20.039/20.039 Maybe level confluent 20.039/20.039 Maybe confluent 20.039/20.039 20.039/20.039 Problem 1: 20.039/20.039 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.039/20.039 Confluence Problem: 20.039/20.039 (STRATEGY CONTEXTSENSITIVE 20.039/20.039 (a) 20.039/20.039 (f 1) 20.039/20.039 (c) 20.039/20.039 (d) 20.039/20.039 (fSNonEmpty) 20.039/20.039 ) 20.039/20.039 (RULES 20.039/20.039 a -> c 20.039/20.039 a -> d 20.039/20.039 ) 20.039/20.039 Critical Pairs: 20.039/20.039 => Not trivial, Overlay, N1 20.039/20.039 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.039/20.039 20.039/20.039 Conditional Critical Pairs Distributor Processor 20.039/20.039 20.039/20.039 Problem 1: 20.039/20.039 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.039/20.039 Confluence Problem: 20.039/20.039 (STRATEGY CONTEXTSENSITIVE 20.039/20.039 (a) 20.039/20.039 (f 1) 20.039/20.039 (c) 20.039/20.039 (d) 20.039/20.039 (fSNonEmpty) 20.039/20.039 ) 20.039/20.039 (RULES 20.039/20.039 a -> c 20.039/20.039 a -> d 20.039/20.039 ) 20.039/20.039 Critical Pairs: 20.039/20.039 => Not trivial, Overlay, N1 20.039/20.039 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.039/20.039 20.039/20.039 InfChecker Different Ground and Normal No Conditions CCP Terms Processor: 20.039/20.039 Proof: 20.039/20.039 YES 20.039/20.039 20.039/20.039 Problem 1: 20.039/20.039 20.039/20.039 Infeasibility Problem: 20.039/20.039 [(VAR vNonEmpty:S y:S) 20.039/20.039 (STRATEGY CONTEXTSENSITIVE 20.039/20.039 (a) 20.039/20.039 (c) 20.039/20.039 (d) 20.039/20.039 (fSNonEmpty) 20.039/20.039 ) 20.039/20.039 (RULES 20.039/20.039 a -> c 20.039/20.039 a -> d 20.039/20.039 )] 20.039/20.039 Infeasibility Conditions: 20.039/20.039 c -> y:S 20.039/20.039 20.039/20.039 Problem 1: 20.039/20.039 20.039/20.039 Obtaining a model using Mace4: 20.039/20.039 20.039/20.039 -> Usable Rules: 20.039/20.039 Empty 20.039/20.039 20.039/20.039 -> Mace4 Output: 20.039/20.039 ============================== Mace4 ================================= 20.039/20.039 Mace4 (64) version 2009-11A, November 2009. 20.039/20.039 Process 48429 was started by ubuntu on ubuntu, 20.039/20.039 Wed Jul 14 10:47:48 2021 20.039/20.039 The command was "./mace4 -c -f /tmp/mace448402-2.in". 20.039/20.039 ============================== end of head =========================== 20.039/20.039 20.039/20.039 ============================== INPUT ================================= 20.039/20.039 20.039/20.039 % Reading from file /tmp/mace448402-2.in 20.039/20.039 20.039/20.039 assign(max_seconds,6). 20.039/20.039 20.039/20.039 formulas(assumptions). 20.039/20.039 end_of_list. 20.039/20.039 20.039/20.039 formulas(goals). 20.039/20.039 (exists x1 ->(c,x1)) # label(goal). 20.039/20.039 end_of_list. 20.039/20.039 20.039/20.039 ============================== end of input ========================== 20.039/20.039 20.039/20.039 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 20.039/20.039 20.039/20.039 % Formulas that are not ordinary clauses: 20.039/20.039 1 (exists x1 ->(c,x1)) # label(goal) # label(non_clause) # label(goal). [goal]. 20.039/20.039 20.039/20.039 ============================== end of process non-clausal formulas === 20.039/20.039 20.039/20.039 ============================== CLAUSES FOR SEARCH ==================== 20.039/20.039 20.039/20.039 formulas(mace4_clauses). 20.039/20.039 -->(c,x) # label(goal). 20.039/20.039 end_of_list. 20.039/20.039 20.039/20.039 ============================== end of clauses for search ============= 20.039/20.039 20.039/20.039 % There are no natural numbers in the input. 20.039/20.039 20.039/20.039 ============================== DOMAIN SIZE 2 ========================= 20.039/20.039 20.039/20.039 ============================== MODEL ================================= 20.039/20.039 20.039/20.039 interpretation( 2, [number=1, seconds=0], [ 20.039/20.039 20.039/20.039 function(c, [ 0 ]), 20.039/20.039 20.039/20.039 relation(->(_,_), [ 20.039/20.039 0, 0, 20.039/20.039 0, 0 ]) 20.039/20.039 ]). 20.039/20.039 20.039/20.039 ============================== end of model ========================== 20.039/20.039 20.039/20.039 ============================== STATISTICS ============================ 20.039/20.039 20.039/20.039 For domain size 2. 20.039/20.039 20.039/20.039 Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds). 20.039/20.039 Ground clauses: seen=2, kept=2. 20.039/20.039 Selections=3, assignments=3, propagations=2, current_models=1. 20.039/20.039 Rewrite_terms=2, rewrite_bools=2, indexes=2. 20.039/20.039 Rules_from_neg_clauses=0, cross_offs=0. 20.039/20.039 20.039/20.039 ============================== end of statistics ===================== 20.039/20.039 20.039/20.039 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 20.039/20.039 20.039/20.039 Exiting with 1 model. 20.039/20.039 20.039/20.039 Process 48429 exit (max_models) Wed Jul 14 10:47:48 2021 20.039/20.039 The process finished Wed Jul 14 10:47:48 2021 20.039/20.039 20.039/20.039 20.039/20.039 Mace4 cooked interpretation: 20.039/20.039 20.039/20.039 20.039/20.039 20.039/20.039 The problem is infeasible. 20.039/20.039 YES 20.039/20.039 20.039/20.039 Problem 1: 20.039/20.039 20.039/20.039 Infeasibility Problem: 20.039/20.039 [(VAR vNonEmpty:S x:S) 20.039/20.039 (STRATEGY CONTEXTSENSITIVE 20.039/20.039 (a) 20.039/20.039 (c) 20.039/20.039 (d) 20.039/20.039 (fSNonEmpty) 20.039/20.039 ) 20.039/20.039 (RULES 20.039/20.039 a -> c 20.039/20.039 a -> d 20.039/20.039 )] 20.039/20.039 Infeasibility Conditions: 20.039/20.039 d -> x:S 20.039/20.039 20.039/20.039 Problem 1: 20.039/20.039 20.039/20.039 Obtaining a model using Mace4: 20.039/20.039 20.039/20.039 -> Usable Rules: 20.039/20.039 Empty 20.039/20.039 20.039/20.039 -> Mace4 Output: 20.039/20.039 ============================== Mace4 ================================= 20.039/20.039 Mace4 (64) version 2009-11A, November 2009. 20.039/20.039 Process 48465 was started by ubuntu on ubuntu, 20.039/20.039 Wed Jul 14 10:47:48 2021 20.039/20.039 The command was "./mace4 -c -f /tmp/mace448450-2.in". 20.039/20.039 ============================== end of head =========================== 20.039/20.039 20.039/20.039 ============================== INPUT ================================= 20.039/20.039 20.039/20.039 % Reading from file /tmp/mace448450-2.in 20.039/20.039 20.039/20.039 assign(max_seconds,6). 20.039/20.039 20.039/20.039 formulas(assumptions). 20.039/20.039 end_of_list. 20.039/20.039 20.039/20.039 formulas(goals). 20.039/20.039 (exists x1 ->(d,x1)) # label(goal). 20.039/20.039 end_of_list. 20.039/20.039 20.039/20.039 ============================== end of input ========================== 20.039/20.039 20.039/20.039 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 20.039/20.039 20.039/20.039 % Formulas that are not ordinary clauses: 20.039/20.039 1 (exists x1 ->(d,x1)) # label(goal) # label(non_clause) # label(goal). [goal]. 20.039/20.039 20.039/20.039 ============================== end of process non-clausal formulas === 20.039/20.039 20.039/20.039 ============================== CLAUSES FOR SEARCH ==================== 20.039/20.039 20.039/20.039 formulas(mace4_clauses). 20.039/20.039 -->(d,x) # label(goal). 20.039/20.039 end_of_list. 20.039/20.039 20.039/20.039 ============================== end of clauses for search ============= 20.039/20.039 20.039/20.039 % There are no natural numbers in the input. 20.039/20.039 20.039/20.039 ============================== DOMAIN SIZE 2 ========================= 20.039/20.039 20.039/20.039 ============================== MODEL ================================= 20.039/20.039 20.039/20.039 interpretation( 2, [number=1, seconds=0], [ 20.039/20.039 20.039/20.039 function(d, [ 0 ]), 20.039/20.039 20.039/20.039 relation(->(_,_), [ 20.039/20.039 0, 0, 20.039/20.039 0, 0 ]) 20.039/20.039 ]). 20.039/20.039 20.039/20.039 ============================== end of model ========================== 20.039/20.039 20.039/20.039 ============================== STATISTICS ============================ 20.039/20.039 20.039/20.039 For domain size 2. 20.039/20.039 20.039/20.039 Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds). 20.039/20.039 Ground clauses: seen=2, kept=2. 20.039/20.039 Selections=3, assignments=3, propagations=2, current_models=1. 20.039/20.039 Rewrite_terms=2, rewrite_bools=2, indexes=2. 20.039/20.039 Rules_from_neg_clauses=0, cross_offs=0. 20.039/20.039 20.039/20.039 ============================== end of statistics ===================== 20.039/20.039 20.039/20.039 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 20.039/20.039 20.039/20.039 Exiting with 1 model. 20.039/20.039 20.039/20.039 Process 48465 exit (max_models) Wed Jul 14 10:47:48 2021 20.039/20.039 The process finished Wed Jul 14 10:47:48 2021 20.039/20.039 20.039/20.039 20.039/20.039 Mace4 cooked interpretation: 20.039/20.039 20.039/20.039 20.039/20.039 20.039/20.039 The problem is infeasible. 20.039/20.039 20.039/20.039 20.039/20.039 The problem is not joinable. 20.039/20.039 22.87user 0.41system 0:20.39elapsed 114%CPU (0avgtext+0avgdata 138180maxresident)k 20.039/20.039 0inputs+0outputs (0major+83046minor)pagefaults 0swaps