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TRS Standard pair #487066714
details
property
value
status
complete
benchmark
11.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n183.star.cs.uiowa.edu
space
Various_04
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.173655 seconds
cpu usage
0.158582
user time
0.07486
system time
0.083722
max virtual memory
113188.0
max residence set size
6136.0
stage attributes
key
value
starexec-result
YES
output
YES Problem 1: (VAR v_NonEmpty:S x:S y:S) (RULES f(0,1,x:S) -> f(h(x:S),h(x:S),x:S) h(0) -> 0 h(g(x:S,y:S)) -> y:S ) Problem 1: Innermost Equivalent Processor: -> Rules: f(0,1,x:S) -> f(h(x:S),h(x:S),x:S) h(0) -> 0 h(g(x:S,y: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(0,1,x:S) -> F(h(x:S),h(x:S),x:S) F(0,1,x:S) -> H(x:S) -> Rules: f(0,1,x:S) -> f(h(x:S),h(x:S),x:S) h(0) -> 0 h(g(x:S,y:S)) -> y:S Problem 1: SCC Processor: -> Pairs: F(0,1,x:S) -> F(h(x:S),h(x:S),x:S) F(0,1,x:S) -> H(x:S) -> Rules: f(0,1,x:S) -> f(h(x:S),h(x:S),x:S) h(0) -> 0 h(g(x:S,y:S)) -> y:S ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: F(0,1,x:S) -> F(h(x:S),h(x:S),x:S) ->->-> Rules: f(0,1,x:S) -> f(h(x:S),h(x:S),x:S) h(0) -> 0 h(g(x:S,y:S)) -> y:S Problem 1: Reduction Pair Processor: -> Pairs: F(0,1,x:S) -> F(h(x:S),h(x:S),x:S) -> Rules: f(0,1,x:S) -> f(h(x:S),h(x:S),x:S) h(0) -> 0 h(g(x:S,y:S)) -> y:S -> Usable rules: h(0) -> 0 h(g(x:S,y:S)) -> y:S ->Mace4 Output: ============================== Mace4 ================================= Mace4 (64) version 2009-11A, November 2009. Process 20549 was started by sandbox on n183.star.cs.uiowa.edu, Sun Jun 21 22:12:23 2020 The command was "./mace4 -c -f /tmp/mace4336465782861021530.in". ============================== end of head =========================== ============================== INPUT ================================= % Reading from file /tmp/mace4336465782861021530.in assign(max_seconds,20). formulas(assumptions). 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,x2,x3),f2(y,x2,x3)) # label(congruence). arrow_s0(x2,y) -> arrow_s0(f2(x1,x2,x3),f2(x1,y,x3)) # label(congruence). arrow_s0(x3,y) -> arrow_s0(f2(x1,x2,x3),f2(x1,x2,y)) # label(congruence). arrow_s0(x1,y) -> arrow_s0(f3(x1),f3(y)) # label(congruence). arrow_s0(x1,y) -> arrow_s0(f7(x1,x2),f7(y,x2)) # label(congruence). arrow_s0(x2,y) -> arrow_s0(f7(x1,x2),f7(x1,y)) # label(congruence). arrow_s0(x1,y) -> arrow_s0(f9(x1,x2,x3),f9(y,x2,x3)) # label(congruence). arrow_s0(x2,y) -> arrow_s0(f9(x1,x2,x3),f9(x1,y,x3)) # label(congruence). arrow_s0(x3,y) -> arrow_s0(f9(x1,x2,x3),f9(x1,x2,y)) # label(congruence). arrow_s0(x1,y) -> arrow_s0(f10(x1),f10(y)) # label(congruence). arrow_s0(f3(f4),f4) # label(replacement). arrow_s0(f3(f7(x1,x2)),x2) # label(replacement). arrow_s0(x,y) -> gtrsim_s0(x,y) # label(inclusion). sqsupset_s0(f9(f4,f5,x1),f9(f3(x1),f3(x1),x1)) # 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).
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