19.30/5.69 YES 19.30/5.69 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 19.30/5.69 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 19.30/5.69 19.30/5.69 19.30/5.69 Termination of the given RelTRS could be proven: 19.30/5.69 19.30/5.69 (0) RelTRS 19.30/5.69 (1) RelTRSRRRProof [EQUIVALENT, 837 ms] 19.30/5.69 (2) RelTRS 19.30/5.69 (3) RIsEmptyProof [EQUIVALENT, 0 ms] 19.30/5.69 (4) YES 19.30/5.69 19.30/5.69 19.30/5.69 ---------------------------------------- 19.30/5.69 19.30/5.69 (0) 19.30/5.69 Obligation: 19.30/5.69 Relative term rewrite system: 19.30/5.69 The relative TRS consists of the following R rules: 19.30/5.69 19.30/5.69 a(a(b(b(x1)))) -> x1 19.30/5.69 19.30/5.69 The relative TRS consists of the following S rules: 19.30/5.69 19.30/5.69 b(a(x1)) -> a(b(a(b(x1)))) 19.30/5.69 19.30/5.69 19.30/5.69 ---------------------------------------- 19.30/5.69 19.30/5.69 (1) RelTRSRRRProof (EQUIVALENT) 19.30/5.69 We used the following monotonic ordering for rule removal: 19.30/5.69 Matrix interpretation [MATRO] to (N^6, +, *, >=, >) : 19.30/5.69 19.30/5.69 <<< 19.30/5.69 POL(a(x_1)) = [[0], [0], [0], [0], [0], [0]] + [[1, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 1, 0], [0, 0, 0, 1, 0, 1], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]] * x_1 19.30/5.69 >>> 19.30/5.69 19.30/5.69 <<< 19.30/5.69 POL(b(x_1)) = [[0], [1], [0], [0], [0], [0]] + [[1, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1], [0, 1, 0, 0, 0, 0]] * x_1 19.30/5.69 >>> 19.30/5.69 19.30/5.69 With this ordering the following rules can be removed [MATRO] because they are oriented strictly: 19.30/5.69 Rules from R: 19.30/5.69 19.30/5.69 a(a(b(b(x1)))) -> x1 19.30/5.69 Rules from S: 19.30/5.69 none 19.30/5.69 19.30/5.69 19.30/5.69 19.30/5.69 19.30/5.69 ---------------------------------------- 19.30/5.69 19.30/5.69 (2) 19.30/5.69 Obligation: 19.30/5.69 Relative term rewrite system: 19.30/5.69 R is empty. 19.30/5.69 The relative TRS consists of the following S rules: 19.30/5.69 19.30/5.69 b(a(x1)) -> a(b(a(b(x1)))) 19.30/5.69 19.30/5.69 19.30/5.69 ---------------------------------------- 19.30/5.69 19.30/5.69 (3) RIsEmptyProof (EQUIVALENT) 19.30/5.69 The TRS R is empty. Hence, termination is trivially proven. 19.30/5.69 ---------------------------------------- 19.30/5.69 19.30/5.69 (4) 19.30/5.69 YES 19.51/8.69 EOF