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TRS Standard pair #516964411
details
property
value
status
complete
benchmark
test830.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n026.star.cs.uiowa.edu
space
Strategy_removed_mixed_05
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.15331196785 seconds
cpu usage
0.040865925
max memory
3371008.0
stage attributes
key
value
output-size
3776
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(s(X:S)) -> f(X:S) g(cons(0,Y:S)) -> g(Y:S) g(cons(s(X:S),Y:S)) -> s(X:S) h(cons(X:S,Y:S)) -> h(g(cons(X:S,Y:S))) ) Problem 1: Innermost Equivalent Processor: -> Rules: f(s(X:S)) -> f(X:S) g(cons(0,Y:S)) -> g(Y:S) g(cons(s(X:S),Y:S)) -> s(X:S) h(cons(X:S,Y:S)) -> h(g(cons(X:S,Y:S))) -> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination. Problem 1: Dependency Pairs Processor: -> Pairs: F(s(X:S)) -> F(X:S) G(cons(0,Y:S)) -> G(Y:S) H(cons(X:S,Y:S)) -> G(cons(X:S,Y:S)) H(cons(X:S,Y:S)) -> H(g(cons(X:S,Y:S))) -> Rules: f(s(X:S)) -> f(X:S) g(cons(0,Y:S)) -> g(Y:S) g(cons(s(X:S),Y:S)) -> s(X:S) h(cons(X:S,Y:S)) -> h(g(cons(X:S,Y:S))) Problem 1: SCC Processor: -> Pairs: F(s(X:S)) -> F(X:S) G(cons(0,Y:S)) -> G(Y:S) H(cons(X:S,Y:S)) -> G(cons(X:S,Y:S)) H(cons(X:S,Y:S)) -> H(g(cons(X:S,Y:S))) -> Rules: f(s(X:S)) -> f(X:S) g(cons(0,Y:S)) -> g(Y:S) g(cons(s(X:S),Y:S)) -> s(X:S) h(cons(X:S,Y:S)) -> h(g(cons(X:S,Y:S))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: G(cons(0,Y:S)) -> G(Y:S) ->->-> Rules: f(s(X:S)) -> f(X:S) g(cons(0,Y:S)) -> g(Y:S) g(cons(s(X:S),Y:S)) -> s(X:S) h(cons(X:S,Y:S)) -> h(g(cons(X:S,Y:S))) ->->Cycle: ->->-> Pairs: H(cons(X:S,Y:S)) -> H(g(cons(X:S,Y:S))) ->->-> Rules: f(s(X:S)) -> f(X:S) g(cons(0,Y:S)) -> g(Y:S) g(cons(s(X:S),Y:S)) -> s(X:S) h(cons(X:S,Y:S)) -> h(g(cons(X:S,Y:S))) ->->Cycle: ->->-> Pairs: F(s(X:S)) -> F(X:S) ->->-> Rules: f(s(X:S)) -> f(X:S) g(cons(0,Y:S)) -> g(Y:S) g(cons(s(X:S),Y:S)) -> s(X:S) h(cons(X:S,Y:S)) -> h(g(cons(X:S,Y:S))) The problem is decomposed in 3 subproblems. Problem 1.1: Subterm Processor: -> Pairs: G(cons(0,Y:S)) -> G(Y:S) -> Rules: f(s(X:S)) -> f(X:S) g(cons(0,Y:S)) -> g(Y:S) g(cons(s(X:S),Y:S)) -> s(X:S) h(cons(X:S,Y:S)) -> h(g(cons(X:S,Y:S))) ->Projection: pi(G) = 1 Problem 1.1:
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