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TRS Standard pair #516961036
details
property
value
status
complete
benchmark
tpa2.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n056.star.cs.uiowa.edu
space
Secret_05_TRS
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.160788059235 seconds
cpu usage
0.130242266
max memory
4005888.0
stage attributes
key
value
output-size
5666
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 -(s(x:S),s(y:S)) -> -(x:S,y:S) -(x:S,0) -> x:S f(s(x:S),y:S) -> f(p(-(s(x:S),y:S)),p(-(y:S,s(x:S)))) f(x:S,s(y:S)) -> f(p(-(x:S,s(y:S))),p(-(s(y:S),x:S))) p(s(x:S)) -> x:S ) Problem 1: Innermost Equivalent Processor: -> Rules: -(s(x:S),s(y:S)) -> -(x:S,y:S) -(x:S,0) -> x:S f(s(x:S),y:S) -> f(p(-(s(x:S),y:S)),p(-(y:S,s(x:S)))) f(x:S,s(y:S)) -> f(p(-(x:S,s(y:S))),p(-(s(y:S),x:S))) p(s(x:S)) -> x:S -> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination. Problem 1: Dependency Pairs Processor: -> Pairs: -#(s(x:S),s(y:S)) -> -#(x:S,y:S) F(s(x:S),y:S) -> -#(s(x:S),y:S) F(s(x:S),y:S) -> -#(y:S,s(x:S)) F(s(x:S),y:S) -> F(p(-(s(x:S),y:S)),p(-(y:S,s(x:S)))) F(s(x:S),y:S) -> P(-(s(x:S),y:S)) F(s(x:S),y:S) -> P(-(y:S,s(x:S))) F(x:S,s(y:S)) -> -#(s(y:S),x:S) F(x:S,s(y:S)) -> -#(x:S,s(y:S)) F(x:S,s(y:S)) -> F(p(-(x:S,s(y:S))),p(-(s(y:S),x:S))) F(x:S,s(y:S)) -> P(-(s(y:S),x:S)) F(x:S,s(y:S)) -> P(-(x:S,s(y:S))) -> Rules: -(s(x:S),s(y:S)) -> -(x:S,y:S) -(x:S,0) -> x:S f(s(x:S),y:S) -> f(p(-(s(x:S),y:S)),p(-(y:S,s(x:S)))) f(x:S,s(y:S)) -> f(p(-(x:S,s(y:S))),p(-(s(y:S),x:S))) p(s(x:S)) -> x:S Problem 1: SCC Processor: -> Pairs: -#(s(x:S),s(y:S)) -> -#(x:S,y:S) F(s(x:S),y:S) -> -#(s(x:S),y:S) F(s(x:S),y:S) -> -#(y:S,s(x:S)) F(s(x:S),y:S) -> F(p(-(s(x:S),y:S)),p(-(y:S,s(x:S)))) F(s(x:S),y:S) -> P(-(s(x:S),y:S)) F(s(x:S),y:S) -> P(-(y:S,s(x:S))) F(x:S,s(y:S)) -> -#(s(y:S),x:S) F(x:S,s(y:S)) -> -#(x:S,s(y:S)) F(x:S,s(y:S)) -> F(p(-(x:S,s(y:S))),p(-(s(y:S),x:S))) F(x:S,s(y:S)) -> P(-(s(y:S),x:S)) F(x:S,s(y:S)) -> P(-(x:S,s(y:S))) -> Rules: -(s(x:S),s(y:S)) -> -(x:S,y:S) -(x:S,0) -> x:S f(s(x:S),y:S) -> f(p(-(s(x:S),y:S)),p(-(y:S,s(x:S)))) f(x:S,s(y:S)) -> f(p(-(x:S,s(y:S))),p(-(s(y:S),x:S))) p(s(x:S)) -> x:S ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: -#(s(x:S),s(y:S)) -> -#(x:S,y:S) ->->-> Rules: -(s(x:S),s(y:S)) -> -(x:S,y:S) -(x:S,0) -> x:S f(s(x:S),y:S) -> f(p(-(s(x:S),y:S)),p(-(y:S,s(x:S)))) f(x:S,s(y:S)) -> f(p(-(x:S,s(y:S))),p(-(s(y:S),x:S))) p(s(x:S)) -> x:S ->->Cycle: ->->-> Pairs: F(s(x:S),y:S) -> F(p(-(s(x:S),y:S)),p(-(y:S,s(x:S)))) F(x:S,s(y:S)) -> F(p(-(x:S,s(y:S))),p(-(s(y:S),x:S))) ->->-> Rules: -(s(x:S),s(y:S)) -> -(x:S,y:S) -(x:S,0) -> x:S f(s(x:S),y:S) -> f(p(-(s(x:S),y:S)),p(-(y:S,s(x:S)))) f(x:S,s(y:S)) -> f(p(-(x:S,s(y:S))),p(-(s(y:S),x:S))) p(s(x:S)) -> x:S The problem is decomposed in 2 subproblems. Problem 1.1:
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