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TRS Standard pair #516964546
details
property
value
status
complete
benchmark
beans.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n175.star.cs.uiowa.edu
space
Mixed_TRS
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
3.05786585808 seconds
cpu usage
3.014963196
max memory
7.0017024E7
stage attributes
key
value
output-size
7858
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 w:S x:S y:S z:S) (RULES L(f(s(s(y:S)),f(z:S,w:S))) -> L(f(s(0),f(y:S,f(s(z:S),w:S)))) f(x:S,f(s(s(y:S)),f(z:S,w:S))) -> f(s(x:S),f(y:S,f(s(z:S),w:S))) f(x:S,f(s(s(y:S)),nil)) -> f(s(x:S),f(y:S,f(s(0),nil))) ) Problem 1: Dependency Pairs Processor: -> Pairs: L#(f(s(s(y:S)),f(z:S,w:S))) -> L#(f(s(0),f(y:S,f(s(z:S),w:S)))) L#(f(s(s(y:S)),f(z:S,w:S))) -> F(s(0),f(y:S,f(s(z:S),w:S))) L#(f(s(s(y:S)),f(z:S,w:S))) -> F(s(z:S),w:S) L#(f(s(s(y:S)),f(z:S,w:S))) -> F(y:S,f(s(z:S),w:S)) F(x:S,f(s(s(y:S)),f(z:S,w:S))) -> F(s(x:S),f(y:S,f(s(z:S),w:S))) F(x:S,f(s(s(y:S)),f(z:S,w:S))) -> F(s(z:S),w:S) F(x:S,f(s(s(y:S)),f(z:S,w:S))) -> F(y:S,f(s(z:S),w:S)) F(x:S,f(s(s(y:S)),nil)) -> F(s(x:S),f(y:S,f(s(0),nil))) -> Rules: L(f(s(s(y:S)),f(z:S,w:S))) -> L(f(s(0),f(y:S,f(s(z:S),w:S)))) f(x:S,f(s(s(y:S)),f(z:S,w:S))) -> f(s(x:S),f(y:S,f(s(z:S),w:S))) f(x:S,f(s(s(y:S)),nil)) -> f(s(x:S),f(y:S,f(s(0),nil))) Problem 1: SCC Processor: -> Pairs: L#(f(s(s(y:S)),f(z:S,w:S))) -> L#(f(s(0),f(y:S,f(s(z:S),w:S)))) L#(f(s(s(y:S)),f(z:S,w:S))) -> F(s(0),f(y:S,f(s(z:S),w:S))) L#(f(s(s(y:S)),f(z:S,w:S))) -> F(s(z:S),w:S) L#(f(s(s(y:S)),f(z:S,w:S))) -> F(y:S,f(s(z:S),w:S)) F(x:S,f(s(s(y:S)),f(z:S,w:S))) -> F(s(x:S),f(y:S,f(s(z:S),w:S))) F(x:S,f(s(s(y:S)),f(z:S,w:S))) -> F(s(z:S),w:S) F(x:S,f(s(s(y:S)),f(z:S,w:S))) -> F(y:S,f(s(z:S),w:S)) F(x:S,f(s(s(y:S)),nil)) -> F(s(x:S),f(y:S,f(s(0),nil))) -> Rules: L(f(s(s(y:S)),f(z:S,w:S))) -> L(f(s(0),f(y:S,f(s(z:S),w:S)))) f(x:S,f(s(s(y:S)),f(z:S,w:S))) -> f(s(x:S),f(y:S,f(s(z:S),w:S))) f(x:S,f(s(s(y:S)),nil)) -> f(s(x:S),f(y:S,f(s(0),nil))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: F(x:S,f(s(s(y:S)),f(z:S,w:S))) -> F(s(x:S),f(y:S,f(s(z:S),w:S))) F(x:S,f(s(s(y:S)),f(z:S,w:S))) -> F(s(z:S),w:S) F(x:S,f(s(s(y:S)),f(z:S,w:S))) -> F(y:S,f(s(z:S),w:S)) F(x:S,f(s(s(y:S)),nil)) -> F(s(x:S),f(y:S,f(s(0),nil))) ->->-> Rules: L(f(s(s(y:S)),f(z:S,w:S))) -> L(f(s(0),f(y:S,f(s(z:S),w:S)))) f(x:S,f(s(s(y:S)),f(z:S,w:S))) -> f(s(x:S),f(y:S,f(s(z:S),w:S))) f(x:S,f(s(s(y:S)),nil)) -> f(s(x:S),f(y:S,f(s(0),nil))) ->->Cycle: ->->-> Pairs: L#(f(s(s(y:S)),f(z:S,w:S))) -> L#(f(s(0),f(y:S,f(s(z:S),w:S)))) ->->-> Rules: L(f(s(s(y:S)),f(z:S,w:S))) -> L(f(s(0),f(y:S,f(s(z:S),w:S)))) f(x:S,f(s(s(y:S)),f(z:S,w:S))) -> f(s(x:S),f(y:S,f(s(z:S),w:S))) f(x:S,f(s(s(y:S)),nil)) -> f(s(x:S),f(y:S,f(s(0),nil))) The problem is decomposed in 2 subproblems. Problem 1.1: Reduction Pair Processor: -> Pairs: F(x:S,f(s(s(y:S)),f(z:S,w:S))) -> F(s(x:S),f(y:S,f(s(z:S),w:S))) F(x:S,f(s(s(y:S)),f(z:S,w:S))) -> F(s(z:S),w:S) F(x:S,f(s(s(y:S)),f(z:S,w:S))) -> F(y:S,f(s(z:S),w:S)) F(x:S,f(s(s(y:S)),nil)) -> F(s(x:S),f(y:S,f(s(0),nil))) -> Rules: L(f(s(s(y:S)),f(z:S,w:S))) -> L(f(s(0),f(y:S,f(s(z:S),w:S)))) f(x:S,f(s(s(y:S)),f(z:S,w:S))) -> f(s(x:S),f(y:S,f(s(z:S),w:S))) f(x:S,f(s(s(y:S)),nil)) -> f(s(x:S),f(y:S,f(s(0),nil))) -> Usable rules: f(x:S,f(s(s(y:S)),f(z:S,w:S))) -> f(s(x:S),f(y:S,f(s(z:S),w:S))) f(x:S,f(s(s(y:S)),nil)) -> f(s(x:S),f(y:S,f(s(0),nil))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [f](X1,X2) = 2.X1 + X2 [0] = 0 [nil] = 1
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