TRS Conditional pair #487562995

details

property	value
status	complete
benchmark	ohl.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n100.star.cs.uiowa.edu
space	Mixed_CTRS_2014

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	41.7599029541 seconds
cpu usage	41.641957798
max memory	4.6465024E7

stage attributes

key	value
output-size	4982
starexec-result	YES

output

/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 y:S)
(RULES
f(k(a),k(b),x:S) -> f(x:S,x:S,x:S)
g(x:S) -> k(y:S) | h(x:S) ->* d, h(x:S) ->* c(y:S)
h(d) -> c(a)
h(d) -> c(b)
)

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

Problem 1: 

Dependency Pairs Processor:

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

Conditional Termination Problem 2:
-> Pairs:
 G(x:S) -> H(x:S)
 G(x:S) -> H(x:S) | h(x:S) ->* d
-> QPairs:
 Empty
-> Rules:
 f(k(a),k(b),x:S) -> f(x:S,x:S,x:S)
 g(x:S) -> k(y:S) | h(x:S) ->* d, h(x:S) ->* c(y:S)
 h(d) -> c(a)
 h(d) -> c(b)


The problem is decomposed in 2 subproblems.

Problem 1.1: 

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

Problem 1.1: 

Unsatisfiable Rule Processor:
-> Pairs:
 F(k(a),k(b),x:S) -> F(x:S,x:S,x:S)
-> QPairs:
 Empty
-> Rules:
 f(k(a),k(b),x:S) -> f(x:S,x:S,x:S)
 g(x:S) -> k(y:S) | h(x:S) ->* d, h(x:S) ->* c(y:S)
 h(d) -> c(a)
 h(d) -> c(b)
->AGES Output:
 
Model Results

System:
mod InTheory is
  sorts S Bool .

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