/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


--------------------------------------------------------------------------------


YES

Problem 1: 

(VAR v_NonEmpty:S x:S)
(RULES
f(x:S) -> c | a ->* b
g(x:S,x:S) -> g(f(a),f(b))
)

Problem 1: 
Valid CTRS Processor:
-> Rules:
 f(x:S) -> c | a ->* b
 g(x:S,x:S) -> g(f(a),f(b))
-> The system is a deterministic 3-CTRS.

Problem 1: 

Dependency Pairs Processor:

Conditional Termination Problem 1:
-> Pairs:
 G(x:S,x:S) -> F(a)
 G(x:S,x:S) -> F(b)
 G(x:S,x:S) -> G(f(a),f(b))
-> QPairs:
 Empty
-> Rules:
 f(x:S) -> c | a ->* b
 g(x:S,x:S) -> g(f(a),f(b))

Conditional Termination Problem 2:
-> Pairs:
 Empty
-> QPairs:
 Empty
-> Rules:
 f(x:S) -> c | a ->* b
 g(x:S,x:S) -> g(f(a),f(b))


The problem is decomposed in 2 subproblems.

Problem 1.1: 

SCC Processor:
-> Pairs:
 G(x:S,x:S) -> F(a)
 G(x:S,x:S) -> F(b)
 G(x:S,x:S) -> G(f(a),f(b))
-> QPairs:
 Empty
-> Rules:
 f(x:S) -> c | a ->* b
 g(x:S,x:S) -> g(f(a),f(b))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 G(x:S,x:S) -> G(f(a),f(b))
-> QPairs:
 Empty
->->-> Rules:
 f(x:S) -> c | a ->* b
 g(x:S,x:S) -> g(f(a),f(b))

Problem 1.1: 

Reduction Pair Processor:
-> Pairs:
 G(x:S,x:S) -> G(f(a),f(b))
-> Rules:
 f(x:S) -> c | a ->* b
 g(x:S,x:S) -> g(f(a),f(b))
-> Needed rules:
 f(x:S) -> c | a ->* b
-> Usable rules:
 Empty
->Mace4 Output:
 ============================== Mace4 =================================
Mace4 (64) version 2009-11A, November 2009.
Process 52533 was started by sandbox on n081.star.cs.uiowa.edu,
Wed Jul  1 10:31:50 2020
The command was "./mace4 -c -f /tmp/mace41957747793424238335.in".
============================== end of head ===========================

============================== INPUT =================================

% Reading from file /tmp/mace41957747793424238335.in

assign(max_seconds,20).

formulas(assumptions).
arrowStar_s0(x,x) # label(reflexivity).
arrow_s0(x,y) & arrowStar_s0(y,z) -> arrowStar_s0(x,z) # label(compatibility).
gtrsim_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility).
succeq_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility).
gtrsim_s0(x,y) & succeq_s0(y,z) -> gtrsim_s0(x,z) # label(compatibility).
arrow_s0(x1,y) -> arrow_s0(f2(x1),f2(y)) # label(congruence).
arrow_s0(x1,y) -> arrow_s0(f3(x1,x2),f3(y,x2)) # label(congruence).
arrow_s0(x2,y) -> arrow_s0(f3(x1,x2),f3(x1,y)) # label(congruence).
arrow_s0(x1,y) -> arrow_s0(f12(x1,x2),f12(y,x2)) # label(congruence).
arrow_s0(x2,y) -> arrow_s0(f12(x1,x2),f12(x1,y)) # label(congruence).
arrowN_s0(x1,y) -> arrowN_s0(f2(x1),f2(y)) # label(congruence).
arrowN_s0(x1,y) -> arrowN_s0(f3(x1,x2),f3(y,x2)) # label(congruence).
arrowN_s0(x2,y) -> arrowN_s0(f3(x1,x2),f3(x1,y)) # label(congruence).
arrowN_s0(x1,y) -> arrowN_s0(f10(x1),f10(y)) # label(congruence).
arrowN_s0(x1,y) -> arrowN_s0(f11(x1,x2),f11(y,x2)) # label(congruence).
arrowN_s0(x2,y) -> arrowN_s0(f11(x1,x2),f11(x1,y)) # label(congruence).
arrowN_s0(x1,y) -> arrowN_s0(f12(x1,x2),f12(y,x2)) # label(congruence).
arrowN_s0(x2,y) -> arrowN_s0(f12(x1,x2),f12(x1,y)) # label(congruence).
arrow_s0(f12(x2,x3),x2) # label(replacement).
arrow_s0(f12(x2,x3),x3) # label(replacement).
arrowStar_s0(f4,f5) -> arrowN_s0(f2(x1),f6) # label(replacement).
arrowN_s0(f12(x2,x3),x2) # label(replacement).
arrowN_s0(f12(x2,x3),x3) # label(replacement).
arrowN_s0(x,y) -> gtrsim_s0(x,y) # label(inclusion).
sqsupset_s0(f11(x1,x1),f11(f2(f4),f2(f5))) # label(replacement).
sqsupset_s0(x,y) -> sqsupsetStar_s0(x,y) # label(inclusion).
sqsupset_s0(x,y) & sqsupsetStar_s0(y,z) -> sqsupsetStar_s0(x,z) # label(compatibility).
end_of_list.

formulas(goals).
(exists x sqsupsetStar_s0(x,x)) # label(wellfoundedness).
end_of_list.

============================== end of input ==========================

============================== PROCESS NON-CLAUSAL FORMULAS ==========

% Formulas that are not ordinary clauses:
1 arrow_s0(x,y) & arrowStar_s0(y,z) -> arrowStar_s0(x,z) # label(compatibility) # label(non_clause).  [assumption].
2 gtrsim_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility) # label(non_clause).  [assumption].
3 succeq_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility) # label(non_clause).  [assumption].
4 gtrsim_s0(x,y) & succeq_s0(y,z) -> gtrsim_s0(x,z) # label(compatibility) # label(non_clause).  [assumption].
5 arrow_s0(x1,y) -> arrow_s0(f2(x1),f2(y)) # label(congruence) # label(non_clause).  [assumption].
6 arrow_s0(x1,y) -> arrow_s0(f3(x1,x2),f3(y,x2)) # label(congruence) # label(non_clause).  [assumption].
7 arrow_s0(x2,y) -> arrow_s0(f3(x1,x2),f3(x1,y)) # label(congruence) # label(non_clause).  [assumption].
8 arrow_s0(x1,y) -> arrow_s0(f12(x1,x2),f12(y,x2)) # label(congruence) # label(non_clause).  [assumption].
9 arrow_s0(x2,y) -> arrow_s0(f12(x1,x2),f12(x1,y)) # label(congruence) # label(non_clause).  [assumption].
10 arrowN_s0(x1,y) -> arrowN_s0(f2(x1),f2(y)) # label(congruence) # label(non_clause).  [assumption].
11 arrowN_s0(x1,y) -> arrowN_s0(f3(x1,x2),f3(y,x2)) # label(congruence) # label(non_clause).  [assumption].
12 arrowN_s0(x2,y) -> arrowN_s0(f3(x1,x2),f3(x1,y)) # label(congruence) # label(non_clause).  [assumption].
13 arrowN_s0(x1,y) -> arrowN_s0(f10(x1),f10(y)) # label(congruence) # label(non_clause).  [assumption].
14 arrowN_s0(x1,y) -> arrowN_s0(f11(x1,x2),f11(y,x2)) # label(congruence) # label(non_clause).  [assumption].
15 arrowN_s0(x2,y) -> arrowN_s0(f11(x1,x2),f11(x1,y)) # label(congruence) # label(non_clause).  [assumption].
16 arrowN_s0(x1,y) -> arrowN_s0(f12(x1,x2),f12(y,x2)) # label(congruence) # label(non_clause).  [assumption].
17 arrowN_s0(x2,y) -> arrowN_s0(f12(x1,x2),f12(x1,y)) # label(congruence) # label(non_clause).  [assumption].
18 arrowStar_s0(f4,f5) -> arrowN_s0(f2(x1),f6) # label(replacement) # label(non_clause).  [assumption].
19 arrowN_s0(x,y) -> gtrsim_s0(x,y) # label(inclusion) # label(non_clause).  [assumption].
20 sqsupset_s0(x,y) -> sqsupsetStar_s0(x,y) # label(inclusion) # label(non_clause).  [assumption].
21 sqsupset_s0(x,y) & sqsupsetStar_s0(y,z) -> sqsupsetStar_s0(x,z) # label(compatibility) # label(non_clause).  [assumption].
22 (exists x sqsupsetStar_s0(x,x)) # label(wellfoundedness) # label(non_clause) # label(goal).  [goal].

============================== end of process non-clausal formulas ===

============================== CLAUSES FOR SEARCH ====================

formulas(mace4_clauses).
arrowStar_s0(x,x) # label(reflexivity).
-arrow_s0(x,y) | -arrowStar_s0(y,z) | arrowStar_s0(x,z) # label(compatibility).
-gtrsim_s0(x,y) | -sqsupset_s0(y,z) | sqsupset_s0(x,z) # label(compatibility).
-succeq_s0(x,y) | -sqsupset_s0(y,z) | sqsupset_s0(x,z) # label(compatibility).
-gtrsim_s0(x,y) | -succeq_s0(y,z) | gtrsim_s0(x,z) # label(compatibility).
-arrow_s0(x,y) | arrow_s0(f2(x),f2(y)) # label(congruence).
-arrow_s0(x,y) | arrow_s0(f3(x,z),f3(y,z)) # label(congruence).
-arrow_s0(x,y) | arrow_s0(f3(z,x),f3(z,y)) # label(congruence).
-arrow_s0(x,y) | arrow_s0(f12(x,z),f12(y,z)) # label(congruence).
-arrow_s0(x,y) | arrow_s0(f12(z,x),f12(z,y)) # label(congruence).
-arrowN_s0(x,y) | arrowN_s0(f2(x),f2(y)) # label(congruence).
-arrowN_s0(x,y) | arrowN_s0(f3(x,z),f3(y,z)) # label(congruence).
-arrowN_s0(x,y) | arrowN_s0(f3(z,x),f3(z,y)) # label(congruence).
-arrowN_s0(x,y) | arrowN_s0(f10(x),f10(y)) # label(congruence).
-arrowN_s0(x,y) | arrowN_s0(f11(x,z),f11(y,z)) # label(congruence).
-arrowN_s0(x,y) | arrowN_s0(f11(z,x),f11(z,y)) # label(congruence).
-arrowN_s0(x,y) | arrowN_s0(f12(x,z),f12(y,z)) # label(congruence).
-arrowN_s0(x,y) | arrowN_s0(f12(z,x),f12(z,y)) # label(congruence).
arrow_s0(f12(x,y),x) # label(replacement).
arrow_s0(f12(x,y),y) # label(replacement).
-arrowStar_s0(f4,f5) | arrowN_s0(f2(x),f6) # label(replacement).
arrowN_s0(f12(x,y),x) # label(replacement).
arrowN_s0(f12(x,y),y) # label(replacement).
-arrowN_s0(x,y) | gtrsim_s0(x,y) # label(inclusion).
sqsupset_s0(f11(x,x),f11(f2(f4),f2(f5))) # label(replacement).
-sqsupset_s0(x,y) | sqsupsetStar_s0(x,y) # label(inclusion).
-sqsupset_s0(x,y) | -sqsupsetStar_s0(y,z) | sqsupsetStar_s0(x,z) # label(compatibility).
-sqsupsetStar_s0(x,x) # label(wellfoundedness).
end_of_list.

============================== end of clauses for search =============

% There are no natural numbers in the input.

============================== DOMAIN SIZE 2 =========================

============================== STATISTICS ============================

For domain size 2.

Current CPU time: 0.00 seconds (total CPU time: 0.01 seconds).
Ground clauses: seen=164, kept=160.
Selections=1008, assignments=2015, propagations=3376, current_models=0.
Rewrite_terms=16970, rewrite_bools=22034, indexes=4032.
Rules_from_neg_clauses=1102, cross_offs=1102.

============================== end of statistics =====================

============================== DOMAIN SIZE 3 =========================

============================== MODEL =================================

interpretation( 3, [number=1, seconds=0], [

        function(f4, [ 0 ]),

        function(f5, [ 1 ]),

        function(f6, [ 0 ]),

        function(f10(_), [ 0, 0, 0 ]),

        function(f2(_), [ 0, 1, 2 ]),

        function(f11(_,_), [
			   0, 1, 2,
			   0, 0, 0,
			   0, 2, 2 ]),

        function(f12(_,_), [
			   0, 2, 2,
			   2, 1, 2,
			   2, 2, 2 ]),

        function(f3(_,_), [
			   0, 0, 0,
			   0, 0, 0,
			   0, 0, 0 ]),

        relation(arrowN_s0(_,_), [
			   1, 0, 0,
			   0, 1, 0,
			   1, 1, 1 ]),

        relation(arrowStar_s0(_,_), [
			   1, 0, 0,
			   0, 1, 0,
			   1, 1, 1 ]),

        relation(arrow_s0(_,_), [
			   1, 0, 0,
			   0, 1, 0,
			   1, 1, 1 ]),

        relation(gtrsim_s0(_,_), [
			   1, 0, 0,
			   0, 1, 0,
			   1, 1, 1 ]),

        relation(sqsupsetStar_s0(_,_), [
			   0, 1, 0,
			   0, 0, 0,
			   0, 1, 0 ]),

        relation(sqsupset_s0(_,_), [
			   0, 1, 0,
			   0, 0, 0,
			   0, 1, 0 ]),

        relation(succeq_s0(_,_), [
			   0, 0, 0,
			   0, 0, 0,
			   0, 0, 0 ])
]).

============================== end of model ==========================

============================== STATISTICS ============================

For domain size 3.

Current CPU time: 0.00 seconds (total CPU time: 0.01 seconds).
Ground clauses: seen=498, kept=489.
Selections=77, assignments=165, propagations=158, current_models=1.
Rewrite_terms=1639, rewrite_bools=1423, indexes=235.
Rules_from_neg_clauses=20, cross_offs=73.

============================== end of statistics =====================

User_CPU=0.01, System_CPU=0.00, Wall_clock=0.

Exiting with 1 model.

Process 52533 exit (max_models) Wed Jul  1 10:31:50 2020
The process finished Wed Jul  1 10:31:50 2020


Mace4 cooked interpretation:

% number = 1
% seconds = 0

% Interpretation of size 3

f4 = 0.

f5 = 1.

f6 = 0.

f10(0) = 0.
f10(1) = 0.
f10(2) = 0.

f2(0) = 0.
f2(1) = 1.
f2(2) = 2.

f11(0,0) = 0.
f11(0,1) = 1.
f11(0,2) = 2.
f11(1,0) = 0.
f11(1,1) = 0.
f11(1,2) = 0.
f11(2,0) = 0.
f11(2,1) = 2.
f11(2,2) = 2.

f12(0,0) = 0.
f12(0,1) = 2.
f12(0,2) = 2.
f12(1,0) = 2.
f12(1,1) = 1.
f12(1,2) = 2.
f12(2,0) = 2.
f12(2,1) = 2.
f12(2,2) = 2.

f3(0,0) = 0.
f3(0,1) = 0.
f3(0,2) = 0.
f3(1,0) = 0.
f3(1,1) = 0.
f3(1,2) = 0.
f3(2,0) = 0.
f3(2,1) = 0.
f3(2,2) = 0.

  arrowN_s0(0,0).
- arrowN_s0(0,1).
- arrowN_s0(0,2).
- arrowN_s0(1,0).
  arrowN_s0(1,1).
- arrowN_s0(1,2).
  arrowN_s0(2,0).
  arrowN_s0(2,1).
  arrowN_s0(2,2).

  arrowStar_s0(0,0).
- arrowStar_s0(0,1).
- arrowStar_s0(0,2).
- arrowStar_s0(1,0).
  arrowStar_s0(1,1).
- arrowStar_s0(1,2).
  arrowStar_s0(2,0).
  arrowStar_s0(2,1).
  arrowStar_s0(2,2).

  arrow_s0(0,0).
- arrow_s0(0,1).
- arrow_s0(0,2).
- arrow_s0(1,0).
  arrow_s0(1,1).
- arrow_s0(1,2).
  arrow_s0(2,0).
  arrow_s0(2,1).
  arrow_s0(2,2).

  gtrsim_s0(0,0).
- gtrsim_s0(0,1).
- gtrsim_s0(0,2).
- gtrsim_s0(1,0).
  gtrsim_s0(1,1).
- gtrsim_s0(1,2).
  gtrsim_s0(2,0).
  gtrsim_s0(2,1).
  gtrsim_s0(2,2).

- sqsupsetStar_s0(0,0).
  sqsupsetStar_s0(0,1).
- sqsupsetStar_s0(0,2).
- sqsupsetStar_s0(1,0).
- sqsupsetStar_s0(1,1).
- sqsupsetStar_s0(1,2).
- sqsupsetStar_s0(2,0).
  sqsupsetStar_s0(2,1).
- sqsupsetStar_s0(2,2).

- sqsupset_s0(0,0).
  sqsupset_s0(0,1).
- sqsupset_s0(0,2).
- sqsupset_s0(1,0).
- sqsupset_s0(1,1).
- sqsupset_s0(1,2).
- sqsupset_s0(2,0).
  sqsupset_s0(2,1).
- sqsupset_s0(2,2).

- succeq_s0(0,0).
- succeq_s0(0,1).
- succeq_s0(0,2).
- succeq_s0(1,0).
- succeq_s0(1,1).
- succeq_s0(1,2).
- succeq_s0(2,0).
- succeq_s0(2,1).
- succeq_s0(2,2).


Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> QPairs:
 Empty
-> Rules:
 f(x:S) -> c | a ->* b
 g(x:S,x:S) -> g(f(a),f(b))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

SCC Processor:
-> Pairs:
 Empty
-> QPairs:
 Empty
-> Rules:
 f(x:S) -> c | a ->* b
 g(x:S,x:S) -> g(f(a),f(b))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.